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Cryptarithm A cryptarithm is a type of mathematical puzzle in which most or all of the digits in a mathematical expression, such as a sum, sum, are substituted by letters letters or other symbols. symbols. In a typical puzzle, there is a one-to-one correspondence between the numbers and the letters or symbols replacing them. That is, the same digit is always always represented by the same letter or symbol. symbol. The objective of the puzzle is to break the code used. used. That is, to replace each each letter of the cryptarithm cryptarithm by a numeral so that the resulting mathematical expression expression is true. Cryptarithms may have have several solutions. However, there are elegant ones with only one unique solution. Cryptarithm was originally called crypt-arithmetic, a word used by M. Vatriquant ( pseudonym Minos), in the May 1931 issue of Sphinx , a Belgian magazine of recreational mathematics published in French. Later, this word word has been shortened shortened to cryptarithm. cryptarithm. In 1955, J. A. H. Hunter introduced the word alphametic to designate a cryptarithm whose letters form meaningful words or phrases. One of the best known cryptarithm is
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first published in the July 1924 issue of Strand Magazine. This puzzle puzzle was made by the famous puzzlist H. E. Dudeney. This puzzle is also called an alphametic because because the the letters in in the puzzle form a sensible sensible phrase SEND MORE MONEY. This puzzle has the the solution of
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This alphametic or cryptarithm is popular not only onl y because the letters in the puzzle form a very popular phrase, but it has also a unique solution. Solve some of our cryptarithms involving the following words: Puzzle 1. CRYPTARITHM Solve the following cryptarithm cryptarithm,, by substituting each letter with a numeral:
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The are many solutions to this cryptarithm cryptarithm,, one of the solution is: 4
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WHAT IS CRYPTARITHMETIC? Cryptarithmetic is the science and art of creating and solving cryptarithms.
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A cryptarithm is a genre of mathematica mathematicall puzzle in which the digits are replaced by letters of the alphabet or other symbols. The invention of Cryptarithmetic has been ascribed to ancient China. This art was originally known as letter arithmetic or verbal arithmetic. In India, during the Middle Ages, were developed the arithmetical restorations or "skeletons" a type of cryptarithms in which most or all of the digits have been replaced by asterisks. In 1864 the first cryptarithm appeared in the USA, in American Agriculturist. The word cryptarithmetic ("cryptarithmie" in French) was introduced by b y M. Vatriquant, writing under the pseudonym Minos, in the May 1931 issue of Sphinx, a Belgian magazine of recreational mathematics published in French from 1931 to 1939. A type of alphametic addition puzzle termed "doubly-true" was introduced introduced in 1945 by Alan Wayne. It is made up of "number words" that, when read, also form a valid sum. In 1955, J. A. H. Hunter coined the word alphametic to designate a cryptarithm whose letters form sensible words or phrases. The world's best known alphametic puzzle is undoubtedly SEND + MORE = MONEY. It was created by H. E. Dudeney and first published in the July 1924 issue of Strand Magazine associated with the story of a kidnapper's ransom demand. Modernization by introducing innovations such as computers and the Internet is making quite an impact on cryptarithmetic. If you are interested in knowing more about this revolution read the article Will cryptarithmetic survive innovation? HOW TO SOLVE A PUZZLE 1. Preparation Rewrite the problem, expanding the interlinear space to make room for trial numbers that will be written under the letters. l etters. For example, the puzzle SEND + MORE = MONEY, after solving, will appear like this: SEND 9567 +MORE 1085 --------MONEY 10652 2. Remember cryptarithmetic cryptarithmetic conventions Each letter or symbol represents only one digit throughout the problem; When letters are replaced by their digits, the resultant arithmetical operation must be correct; The numerical base, unless specifically stated, is 10; Numbers must not begin with a zero; There must be only one solution to the problem. • •
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3. See subtractions as "upside-down" additions Ease the analysis of subtractions by reading them as upside-down additions. Remember that you can check a subtraction by adding the difference and the subtracter to get the subtrahend: it's the same thing. This subtraction: COUNT -COIN --------SNUB must be read from the bottom to the top and from the right to the left, as if it were this series of additions: B + N = T + C1 U + I = N + C2 N + O = U + C3 S + C = O + C4 C1, C2, C3 and C4 are the carry-overs of "0" or "1" that are to be added to the next column to the left.
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4. Search for "0" and "9" in additions or subtractions A good hint to find zero or 9 is to look for columns containing two or three identical letters. Look at these additions: ***A ***B +***A +***A ------------***A ***B The columns A+A=A and B+A=B indicate that A=zero. In math this is called the "additive identity property of zero"; it says that you add "0" to anything and it doesn't change, therefore it stays the same. Now look at those same additions in the body of the cryptarithm: *A** *B** +*A** +*A** ------------*A** *B** In these cases, we may have A=zero or A=9. It depends whether or not "carry 1" is received from the previous column. In other words, the "9" mimics zero every time it gets a carry-over of "1". 5. Search for "1" in additions or subtractions Look for left hand digits. If single, they are probably "1". Take the world's most famous cryptarithm: SEND +MORE --------MONEY "M" can only equal 1, because it is the "carry 1" from the column S+M=O (+10). In other words, every time an addition of "n" digits gives a total of "n+1" digits, the left hand digit of the total must be "1". In this Madachy's subtraction problem, "C" stands for the digit "1": COUNT -COIN --------SNUB 6. Search for "1" in multiplications or divisions In this multiplication: MAD BE ------MAD RAE ------AMID The first partial product is E x MAD = MAD. Hence "E" must equal "1". In math jargon this is called the "identity" property of "1" in multiplication; you multiply anything by "1" and it doesn't change, therefore it remains the same. Look this division: KT -------NET/LINK NET ------KEKK KTEC ------KEY In the first subtraction, we see K x NET = NET. Then K=1. 7. Search for "1" and "6" in multiplications or divisions
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Any number multiplied by "1" is the number itself. Also, any even number multiplied by "6" is the number itself: 4x1=4 7x1=7 2 x 6 = 2 (+10) 8 x 6 = 8 (+40) Looking at right hand digits of multiplications and divisions, can help you spot digits "1" and "6". Those findings will show like these ones: CB ---------**A **A/***** BC ***C -------------***C **** ***B ***B --------------***** *** The logic is: if C x **A = ***C B x **A = ***B then A=1 or A=6. 8. Search for "0" and "5" in multiplications or divisions Any number multiplied by zero is zero. Also, any odd number multiplied by "5" is "5": 3x0=0 6x0=0 7 x 5 = 5 (+30) 9 x 5 = 5 (+40) Looking at right hand digits of multiplications and divisions, can help you spot digits "0" and "5". Those findings will show like these ones: CB ---------**A **A/***** BC ***A --------------***A **** ***A ***A --------------***** ***
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The logic is: if C x **A = ***A B x **A = ***A then A=0 or A=5 9. Match to make progress Matching is the process of assigning potential values to a variable and testing whether they match the current state of the problem. To see how this works, let's attack this long-hand division: KM ---------AKA/DADDY DYNA --------ARMY ARKA ------RA To facilitate the analysis, let's break it down to its basic components, i.e., 2 multiplications and 2 subtractions: I. K x A K A = D Y N A II. M x A K A = A R K A III.
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ARMY -ARKA --------RA From I and II we get: K x **A = ***A M x **A = ***A This pattern suggests A=0 or A=5. But a look at the divisor "A K A" reveals that A=0 is impossible, because leading letters cannot be zero. Hence A=5. Replacing all A's with "5", subtraction IV becomes: 5RMY -5RK5 --------R5 From column Y-5=5 we get Y=0. Replacing all Y's with zero, multiplication I will be: K x 5K5 =D0N5 Now, matching can help us make some progress. Digits 1, 2, 3, 4, 6, 7, 8 and 9 are still unidentified. Let's assign all these values to the variable K, one by one, and check which of them matches the above pattern. Tabulating all data, we would come to: K x 5K5 = D0N5 ---------------------1 515 515 2 525 1050 3 535 1605 4 545 2180 6 565 3390 SOLUTION --> 7 575 4025 <-- SOLUTION 8 585 4680 9 595 5355
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--------------------- You can see that K=7 is the only viable solution that matches the current pattern of multiplication I, yielding: K x AKA = DYNA 7 575 4025 This solution also identifies two other variables: D=4 and N=2. 10. When stuck, generate-and-test Usually we start solving a cryptarithm by searching for 0, 1, and 9. Then if we are dealing with an easy problem there is enough material to proceed decoding the other digits until a solution is found. This is the exception and not the rule. Most frequently after decoding 1 or 2 letters (and sometimes none) you get stuck. To make progress we must apply the generate-and-testmethod, which consists of the following procedures: 1. List all digits still unidentified; 2. Select a base variable (letter) to start generation; 3. Do a cycle of generation and testing: from the list of still unidentified digits (procedure 1) get one and assign it to the base variable; eliminate it from the list; proceed guessing values for the other variables; test consistency; if not consistent, go to perform the next cycle (procedure 3); if consistent, stop: you have found the solution to the problem. To demonstrate how this method works, let's tackle this J. A. H. Hunter's addition: TAKE A + C AKE ---------KATE The column AAA suggests A=0 or A=9. But column EAEE indicates that A+E=10, hence the only acceptable value for "A" is 9, with E=1. Replacing all "A's" with 9 and all "E's" with 1, we get T9K1 9 + C 9K 1 ---------K9T1 Letter repetition in columns KKT and TCK allows us to set up the following algebraic system of equations: C1 + K + K = T + 10 C3 + T + C = K Obviously C1=1 and C3=1. Solving the equation system we get K+C=8: not much, but we discovered a relationship between the values of "K" and "C" that will help us later. But now we are stuck! It's time to use the "generate-and-test" method. Procedure 1: digits 2,3,4,5,6,7 and 8 are still unidentified; Procedure 2: we select "K" as the base variable; CYCLE #1, procedure 3: column TCK shows that T+C=K and no carry, hence "K" must be a high valued digit. So we enter the list obtained through procedure 1 from the high side, assigning "8" to the base variable "K". Knowing that K+C=8, if K=8 then C=0. But this is an unacceptable value for "C", because the addend "CAKE" would become "0981" and cryptarithmetic conventions say that no number can start with zero. So, we must close this cycle and begin cycle #2. By now, the addition layout and the table summarizing current variable data would look like this: T 9 8 1 CYCLE A E K C T 9 ======================== + 0 9 8 1 #1 9 1 8 [0] ---------89T1 Conflicting values for variables are noted within square brackets. CYCLE #2, procedure 3: assigning "7" to the letter "K" we get C=1 because K+C=8. This is an unacceptable value for "C" considering that we have already fixed E=1. Again we have to close the current cycle and go to cycle #3, with the setup and table showing: • • •
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T 9 7 1 CYCLE A E K C T 9 ======================== + 1 9 7 1 #1 9 1 8 [0] ---------- #2 9 1 7 [1] 79T1 CYCLE #3, procedure 3: assigning "6" to the letter "K" we get C=2 because K+C=8. Testing these values for "K" and "C" in the column TCK, we get C3+T+2+=6 making T=3. Now, testing T in column KKT, we would obtain C1+K+K=T+10 or 1+6+6=T+10, making T=3. This is an acceptable value for T, confirming the previous value T=3 we had already found. So, we have got the final solution to the problem, stopping the routine "generate-and-test". The final layout and table would read 3 9 6 1 CYCLE A E K C T 9 ======================== + 2 9 6 1 #1 9 1 8 [0] ---------- #2 9 1 7 [1] 6 9 3 1 #3 9 1 6 2 3 EXAMPLES WORKED OUT IN DETAIL BY MASTER PUZZLISTS 1. Geoffrey Mott-Smith In "Mathematical Puzzles for Beginners & Enthusiasts"© SEND + MORE -----------MONEY We see at once that M in the total must be 1, since the total of the column SM cannot reach as high as 20. Now if M in this column is replaced by 1, how can we make this column total as much as 10 to provide the 1 carried over to the left below? Only by making S very large: 9 or 8. In either case the letter O must stand for zero: the summation of SM could produce only 10 or 11, but we cannot use 1 for letter O as we have already used it for M. If letter O is zero, then in column EO we cannot reach a total as high as 10, so that there will be no 1 to carry over from this column to SM. Hence S must positively be 9. Since the summation EO gives N, and letter O is zero, N must be 1 greater than E and the column NR must total over 10. To put it into an equation: E + 1 = N From the NR column we can derive the equation: N + R + (+ 1) = E + 10 We have to insert the expression (+ 1) because we don’t know yet whether 1 is carried over from column DE. But we do know that 1 has to be carried over from column NR to EO. Subtract the first equation from the second: R + (+1) = 9 We cannot let R equal 9, since we already have S equal to 9. Therefore we will have to make R equal to 8; hence we know that 1 has to be carried over from column DE. Column DE must total at least 12, since Y cannot be 1 or zero. What values can we give D and E to reach this total? We have already used 9 and 8 elsewhere. The only digits left that are high enough are 7, 6 and 7, 5. But remember that one of these has to be E, and N is 1 greater than E. Hence E must be 5, N must be 6, while D is 7. Then Y turns out to be 2, and the puzzle is completely solved. © Copyright Dover Publications, Inc., New York, 1954, ISBN 0-486-20198-8. 2. Steven Kahan In "Take a Look at a Good Book"©
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EAT + THAT -----------APPLE Since every four-digit number is less than 10,000 and every three-digit number is less than 1,000, the sum of two such numbers is necessarily less than 11,000. This sum, though, is a five-digit number, hence is greater than 10,000. Consequently, A must be 1 and P must be 0. Further, we can conclude that T = 9. Otherwise, we would be adding a number less than 1,000 to one less than 9,000, leaving us short of the requisite total. The units column then produces E = 8 while generating a carryover of 1 into the tens column. Together with the previously found value of A, we learn from the tens column that L = 3. Finally, the hundreds column yields the equation E + H = P + 10, where the "10" is required to accommodate the needed carryover into the thousands column. When the values of E and P are substituted into this relationship, we get 8 + H = 10, from which it follows that H = 2. Therefore, the unique solution of the puzzle turns out to be 819 + 9219 = 10038. © Copyright Baywood Publishing Company, Inc., Amityville, New York, 1996, ISBN 0-89503-142-6. 3. J. A. H. Hunter In "Entertaining Mathematical Teasers and How to Solve Them"© NO GUN + NO ---------HUNT Obviously H = 1. From the NUNN column we must have "carry 1," so G = 9, U = zero. Since we have "carry" zero or 1 or 2 from the ONOT column, correspondingly we have N + U = 10 or 9 or 8. But duplication is not allowed, so N = 8 with "carry 2" from ONOT. Hence, O + O = T + 20 - 8 = T + 12. Testing for T = 2, 4 or 6, we find only T = 2 acceptable, O = 7. So we have 87 + 908 + 87 = 1082. © Copyright Dover Publications, Inc., New York, 1983, ISBN 0-486-24500-4. 4. Maxey Brooke In "150 Puzzles In Crypt-Arithmetic"© ABC x DE ---------FEC DEC ---------HGBC In the second partial product we see D x A = D, hence A = 1. D x C and E x C both end in C, hence C = 5. D and E must be odd. Since both partial products have only three digits, neither can be 9. This leaves only 3 and 7. In the first partial product E x B is a number of two digits while in the second partial product D x B is a number of only one digit. Thus E is larger than D, so E = 7 and D = 3. Since D x B has only one digit, B must be 3 or less. The only two possibilities are 0 and 2. B cannot be zero because 7B is a two-digit number. Thus B = 2. By completing the multiplication, F = 8, E = 7, and G = 6. The answer is 125 x 37 = 4625
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© Copyright Dover Publications, Inc., New York, 1963. 5. Joseph S. Madachy In "Madachy´s Mathematical Recreations"© (B E) (B E) = M O B Here a 3-digit number is the product of a 2-digit number multiplied by itself. Basic knowledge of the laws of multiplication will immediately force the conclusion that B cannot be greater than 3. For if B is 4, and the lowest possible value, 0, is assigned to E then BE = 40. However, (40)(40) = 1,600, a 4-digit number, and the product in the puzzle to be solved has but 3 digits. Convention demands that the initial letters or symbols of alphametics cannot be 0, so B is either 1, 2, or 3. Another convention demands that 2 different letters cannot be substituted for the same digit. That is, if B turns out to be 3, then no other letter in this alphametic could stand for 3. Attention can be directed to E since much can be deduced from the fact that (E)(E) ends in B. If E equals 0, 1, 5, or 6, then the product would be a number ending in 0, 1, 5, or 6, respectively. Since the product, MOB, does not end in E, these numbers for E are eliminated. 2, 3, 4, 7, and 8 can also be eliminated as values for E, since they would yield the terminal digits of 4, 6, or 9 for MOB, and B has been established as being 1, 2, or 3. Only one value for E, 9, remains: (9) (9) = 81 so B = 1, and the alphametic is solved: (BE) (BE) = MOB is (19) (19) = 361. © Copyright Dover Publications, Inc., New York, 1979, ISBN 0-486-23762-1. 6. C. R. Wylie Jr. In "101 Puzzles in Thought & Logic"© ALE x RUM ---------WINE WUWL EWWE ------------ERMPNE To systematize our work we first write in a row the different letters appearing in the problem: ALERUMWINP Over each letter we will write its numerical equivalent when we discover it. In the columns under the various letters we will record clues and tentative hypotheses, being careful to put all related inferences on the same horizontal line. In problems of this sort the digits 0 and 1 can often be found, or at least restricted to a very few possibilities, by simple inspection. For instance, 0 can never occur as the leftmost digit of an integer, and when any number is multiplied by zero the result consists exclusively of zeros. Moreover when any number is multiplied by 1 the result is that number itself. In the present problem, however, we can identify 0 by an even simpler observation. For in the second column from the right, N plus L equals N, with nothing carried over from the column on the right. Hence L must be zero. In our search for 1 we can eliminate R, U, and M at once, since none of these, as multipliers in the second row, reproduces A L E. Moreover E cannot be 1 since U times E does not yield a product ending in U. At present, however, we have no further clues as to whether 1 is A, I, N, P, or W. Now the partial product W U W L ends in L, which we know to be 0. Hence one of the two letters U and E must be 5. Looking at the units digits of the other partial products, we see that both M x E and R x E are numbers ending in E. A moment’s reflection (or a glance at a multiplication table) shows that E must therefore be 5.
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But if E is 5, then both R and M must be odd, since an even number multiplied by 5 would yield a product ending in 0, which is not the case in either the first or third partial product. Moreover, by similar reasoning it is clear that U is an even number. At this point it is convenient to return to our array and list under U the various possibilities, namely 2, 4, 6, and 8. Opposite each of these we record the corresponding value of W as read from the partial product W U W L, whose last two digits are now determined since the factor A L E is known to be _05. These values of W are easily seen to be 1, 2, 3, and 4. From an inspection of the second column from the left we can now deduce the corresponding possibilities for R. As we have already noted, R must be odd; hence its value is twice W plus 1 (the 1 being necessarily carried over from the column on the right). The possible values for R are then 3, 5, 7, and 9, and our array looks like this: 05 ALERUMWINP 32 1 54 2 76 3 98 4 Now in the third column from the left in the example the sum of the digits W, U, and W must be more than 9, since 1 had to be carried over from this column into the column on the left. The values in the first two rows of the array are too low for this, however, hence we can cross out both of these lines. A further consideration of the sum of the digits W, U, and W in the third column from the left, coupled with the fact that M is known to be odd, shows that in the third row of the array M must be 3 while in the fourth row it must be 7. This permits us to reject the third row of the array also, for it contains 3 for both M and W, which is impossible. The correct solution must therefore be the one contained in the fourth row. Hence R is 9, U is 8, M is 7, and W is 4. Substituting these into the problem it is a simple matter to determine that A is 6, I is 2, N is 3, and P is 1. This completes the solution. Accounts bank account is a record of the financial transactions between the customer and the banking institution. The banking institutions have provided several types of accounts to cater to the needs of all sorts of individuals. One of the most important functions of banks is accepting deposits, which is aimed towards generating savings for the purpose of utilizing them in profitable investments. People, on the other hand, also prefer to deposit their savings in the banks, as they can earn interest and also avoid the danger of theft. Types of Bank Accounts Though, the types of accounts offered can vary from bank to bank, here are some of the common bank accounts offered by commercial banks. Checking Account A checking account is also known as a current account or a transactional account. Money deposited in this type of account can be withdrawn at any time, as there in no restriction on the number of withdrawals and the amount of money withdrawn. Customers are generally given paper checks to carry out day-to-day transactions, like paying bills, making purchases, or transferring money to another account. ATM (Automated Teller Machine) facility is also provided to the customers. However, no interest is paid on the deposited money and sometimes, customers have to pay a charge to the banks for rendering this service. This type of account is generally maintained by businessmen or concerns, as they have to make a number of financial transactions each day. A transactional account i s sometimes called a demand deposit account,
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as no notice is required to withdraw money, i.e. money is available on demand. Savings Account Savings accounts are aimed towards mobilizing small savings from the general public. There are certain restrictions regarding the number of withdrawals and the amount to be withdrawn in a particular time period. However, money deposited in this account, earns a fair rate of interest. Though the customers can't withdraw their money with checks, they can avail the ATM facility for the same. A passbook is also provided, which keeps track of all the financial transactions. Money Market Account A money market account is a type of deposit account, in which money can be deposited to earn a higher rate of interest than the savings account. However, a minimum balance is required to be maintained to earn interest and avoid fees. There is also a limit on the number of transactions that can be carried out in a particular month. The customers are usually allowed to make 6 withdrawals per month. Certificate of Deposit A certificate of deposit is also known as time deposit or fixed deposit account. This type of bank account requires the customers to deposit a certain sum of money for a fixed time period. The money deposited in this account can't be withdrawn before the date of maturity. However, some banks allow customers to withdraw money before maturity, by charging a penalty. The rate of interest paid on time deposits is usually higher than the other types of bank accounts. In addition to this, the interest paid on this account depends on the maturity period, i.e. longer the maturity period, the higher is the rate of interest paid. Banking institutions offer several different types of bank accounts to satisfy the individual needs of their customers. These bank accounts enable the public to deposit their money in banks and thereby earn a monetary return. Different Types of Checking Accounts By Allison Boelcke, eHow Contributor Banks offer a variety of checking accounts to suit the needs of its members. Each type of checking account is subject to the bank's requirements, fees and benefits, but there are general guidelines. Personal Personal checking accounts generally fall under two categories: basic and free. o Basic checking accounts have limits on the number of checks that can be written per month and can charge a monthly maintenance fee, while free checking accounts have no limits on checks written or any additional fees. Joint Joint checking accounts are shared by two people, such as spouses or roommates. o They are generally used for household or shared expenses. Student Student checking accounts are offered by banks to high school or college students o with incentives, such as higher interest rates or free checks. Second Chance Second-chance checking accounts are for those with bad credit who cannot obtain o checking accounts elsewhere. Depending on the bank offering the account, an account holder may have to pay a monthly membership fee or keep a minimum balance. Small Business
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Small business checking accounts are for small business owners to pay expenses. To qualify for a small business checking account, a bank will set a limit of monthly transactions, such as less than 200, that will save the account holder from any monthly fees.
***** Definitions of Savings and Checking Accounts By Aksana Nikolai, eHow Contributor Savings and checking accounts allow consumers to put their money in a bank. Understanding the differences and similarities between the two account types helps users successfully manage their finances. Features Checking and savings accounts are deposit accounts. Checking accounts allow o users to deposit and withdraw funds whenever they wish, usually by check or automated teller machine. Savings accounts typically do not allow users to withdraw funds via check or ATM. Function Consumers use checking accounts for frequent transactions and paying bills in the o short term. Savings accounts hold funds set aside for emergencies and/or medium and long-term financial goals, with few withdrawals. Benefits All savings accounts and some checking accounts accumulate interest on balances o held, but savings accounts typically pay more interest than checking accounts. Limitations There is generally no limit placed on the number of transfers and withdrawals o consumers can make per month from a checking account. Savings accounts, however, do have a transaction limit, set by the Federal Reserve to prevent consumers from using a savings account as they would a checking account. Liability Checking and savings accounts make up a portion of a bank's or other deposito taking organization's liabilities, used for issuing loans and making other investments.
****** What Is the Difference Between Checking & Saving Accounts? By Jo Pennypacker, eHow Contributor There used to be definite distinctions between a checking and a saving account. You used a checking account to pay bills and make purchases, whereas a saving account paid interest at various times--monthly, quarterly or yearly--and usually required you to maintain a minimum balance. Today, the differences aren't as great, but there are differences. Interest Even though checking accounts can now earn interest, there are usually o restrictions. You may have to have a minimum balance or make direct deposits so many times a month in order to qualify. A savings account usually earns a higher rate of interest and withdrawals are limited. A minimum balance is still usually required. In fact, the amount of interest you get depends an the amount in your savings account. Check with your bank to see their policies on actual amounts of interest they pay, for both checking--if they offer interest-bearing accounts--and savings. Fees Fees--like interest--apply to both checking and savings accounts unless you o maintain a minimum balance, have direct deposit assigned to the account or open an account online. If you open a checking and savings together, the bank sometimes will waive the fees. If you write checks, there is usually a charge on the check, even if it's only to buy the checks you will use. Transferring Money
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Usually it is faster to transfer money from your checking account than from your savings. Transferring from your savings may take up to five days longer than from your checking account. Check with the bank you're considering setting up an account with to find out its particular policy. Federal regulations restrict some of this activity for savings accounts--they only allow you to make six transfers in a given month.
Debit Cards Debit cards are usually associated with checking accounts. A debit card acts like a credit card, except that rather than running up a bill, the money comes directly from your checking account. Most people use these today in lieu of writing checks. Overdraft Protection You can get overdraft protection for your checking account. This means that if you o write a check for an amount beyond what you have in your checking account, the check won't bounce, which can incur a fee averaging 30 dollars (per check). The bank will either automatically take the money from your savings account or draw on a line of credit if you have one. o
************** The Calculation of Interest on a Savings Account By Ted Martin, eHow Contributor updated: February 26, 2011 Your savings account should be doing more for you than providing a place to salt away your money. A savings account should provide funds back to you, a mechanism called interest. The interest, paid by the bank, is superadded to existing funds in the account periodically. This means your balance grows monthly. The calculation of interest on a savings account has several factors. Average Balance Since balances fluctuate, the bank will use an average, not the high or low figure, o over a specified period. This formula would assess the closing balance each day, sum it and divide the resultant sum by the number of days. APR The annual percentage rate is one customary technique for calculation of interest. o The APR (as it's called) is assigned by the bank. The calculation is elementary. Over the course of the year, $1,000 will garner 1,000 times the interest rate. For example, at 1.9 percent interest, $1,000 will produce $19 in interest in one year. The monthly total is $1.58. APY Average percentage yield is different. APY compounds your interest. Compared to o an APR of 12 percent, each month with APY 1 percent of your balance is aggregated to your account as interest. The same thing happens next month. This means interest on your interest. The resultant rate is higher than 12 percent. Thus a bank can claim, in this case, an APY of about 12.7 percent. Best Interest Seek the highest rate of interest. This provides the most benefit. Be sure to o compare the net yields when contrasting two accounts with similar rates and different types of interest yields. ***************************************************************** Interest Rate Calculation Method By Catlin Tidwell, eHow Contributor updated: December 09, 2010 Interest is money charged on a loan. Calculating an interest rate on a loan can be a complex process. Aside from being able to perform accurate calculations, you need to know whether you are calculating simple or compound interest, the principal value of the loan, the total amount to be repaid, and the number of calculation or compounding periods. Calculating a Simple Interest Rate You can calculate the interest rate being charged in a simple interest loan o calculation using the formula: i = ([A/P]-1)/n. You must know the principal amount
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(P), total amount to be repaid (A), and the number of years payments will be made (n). For example, if you borrowed $1225 (the principal amount) and were to repay a total of $1500 over 3 years, you could calculate the interest as ([1500/1225]-1) / 3 = 0.074, or 7.4% interest. Calculating a Compound Interest Rate You can calculate the interest rate being charged in a compound interest loan o calculation using the formula: i = q(([A/P]^1/nq) - 1). You must know the principal amount (P), total amount to be repaid (A), the number of years payments will be made (n), and the number times per year the interest will be compounded (q). For example, if you borrowed $1225 (the principal amount) and were to repay a total of $1500 over 3 years, with the amount compounded monthly, you could calculate the interest as 12(([1500/1225]^36)-1) = 0.0676 or 6.76% interest. Note when performing your calculation that the caret symbol (^) indicates the number foll owing is an exponent (for example, 2^3 would indicate 2 to the power of 3, or 2 * 2 * 2). Calculating an Interest Rate from APR If you know the annual percentage rate (APR) charged on a loan, you can calculate o interest with the formula: i = q[((1+r)^1/q)-1]. You must know the annual interest rate or APR (r) and the number of times per year the interest will be compounded (q). For example, if your APR were 5% and your payments were compounded monthly, you could calculate the interest as 12[((1+.05)^1/12)-1] = 0.0489, or 4.89% interest. Note when performing your calculation that the caret symbol (^) indicates the number foll owing is an exponent (for example, 2^3 would indicate 2 to the power of 3, or 2 * 2 * 2). ******************************************* Home Loan Interest Rates Interest rate on home loan is something that one has to pay in lieu of the loan provided by the bank/financial institution. Home loan Interest rate is very important element when it comes to choosing a home loan for a customer & it also helps the customer on taking right decision or on pinning down that through which bank or financial institution he or she can go for. Depending on this interest rate, the loan amount and the tenure of the loan, your EMI is calculated which is how you repay your loan to the bank. In case the interest rate is higher, the EMI would be higher and in case the interest rate is lower, the EMI would be lower. Thus y choosing a bank with a lower interest rate, you can certainly increase your monthly savings. But please keep in mind that interest rate is not the only criteria to choose a loan. There are various other parameters as well. The EMI is calculated on a monthly reducing balance method. Your home loan eligibility or how much loan you are eligible for is also calculated on the basis of the interest rates. In case you opt for a bank with a lower interest rate, then your eligibility will be higher compared to a bank that is offering a higher interest rate. Types of Home Loan Interest Rate:1) Fixed Interest Rate : A rate which is set In-advance or which is predetermined for entire term of Home Loan. Let's take an Example : Mr. X has a taken home loan from ABC Bank of Rs. 25 lakhs for 20ys. at an interest rate of 11.50% pa. Then his EMI will be Rs. 26661 which he needs to pay for entire term of loan that is 20 years Please note that most of the fixed home loan interest rates products available in the market are not fully fixed. Most of them come with a reset clause of 3 to 5 years. This means that the interest rates can be reset after a period of every 3 to 5 years (as mentioned in the loan document). . 2) Floating Interest Rate : A rate which is linked to a benchmark rate or the base rate of the bank or the financial institution. The floating home loan interest rate will change as and when the bank will change its benchmark rate or the base rate.
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Let's take an Example : Mr. Y takes a floating rate home loan from ABC Bank of Rs. 25 lakhs for 20yrs. For the initial year the interest rate may be around 9.5% that may change to 10% for the first 4 months of the 2nd year and after that it may change to again. It is not that the rates are always increasing, there are many times, when the clients benefit when the interest rates go down. When the interest rates changes, the customer is given an option to either increase or decrease the tenure or the EMI. In case, the customer chooses to change the EMI, he will spend more when the interest rate increase and will save more when the interest rate decreases. So, here we saw the simple understanding of what is Fixed Rate & Floating/Variable home loan interest rate. Generally, the interest rates for floating rates for home loans are cheaper than interest rate for fixed rates for home loan. Home Loan: Interest Rates Interest rates on home loans depends the amount of loan you want to take. It also depends on the tenure of the loan and whether you are planning to buy a home or you want to buy a plot to construct a home. It may also depend up on the profile of an individual which includes the credit history of the individual. Interest rates differ across various lenders. You will find most of the lender offering you either fixed rate or floating rate home loans.
Fixed rate home loans with a reset clause - These fixed rates are fixed for certain number of years. After that the rates are revised. Fixed rate home loans without reset clause - The interest rates in these home loans are fixed for the entire tenure of loan. Floating rate home loans - Floating rate home loans may change at any given point. In case, the rates revise, the borrower of the loan has an option to either increase/decrease the EMI or to increase/decrease the loan. •
•
•
Guide to Home Loan Interest Rates There are 2 kinds of lenders. Banks (State Bank of India, ICICI Bank, Axis Bank, etc.) and Housing Finance Companies or HFCs (HDFC,LIC Housing Finance, ICICI Home Finance Ltd. ,Dewan Housing Finance, GRUH, etc) Between them there are many kinds of Home Loan rates. Fixed Home Loan rates : In true Fixed RateHome Loans the rates remain fixed throughout the tenure of the loan no matter what. These kind of rates are very expensive (13.50%+ for a 20 year home loan in November 2010) and are offered by a limited number of lenders in the market. Resettable Fixed Rates : Most of the so called Fixed Rates available in the market are of this variety. Here the interest rate is fixed for a period of 2-5 years and is then reset for a further period of 2-5 years and so on. These rates are more reasonable than the true fixed rates dealt with above. You just need to be clear about the nature of fixed rate contract you are getting into. Floating Home Loan rates (also called variable rate loans or adjustable rate loans) For Banks : The effective rate is linked to the Bank's Base Rate. The base rate would have to be declared by the banks at least once every quarter. It is open to each bank to decide its own methodology for fixing the base rate but it is not allowed to change the methodology after
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selecting one methodlogy. The banks will have to document how it has arrived at the base rate and follow the same system consistently. The calculation of the base rate will be open to the RBI for review (which should at least ensure that a set system is actually followed while calculating the Base Rate). This is of course a much better stipulation than the earlier system of BPLR, where no such system was required to be documented by the bank and there was no question of any calculation that could be reviewed by RBI. So even though composition of the base rate from the customer's perspective might continue to remain opaque still it is a better situation than the erstwhile BPLR since the regulator will ensure calculation of Base rate is done in a consistent and fair manner. RBI has banned lending below Base rates except limited categories of loans such as employee loans, loan against its own fixed deposits, Differential Interest rate loans to SC/ST, etc.. The advantage therefore from the consumer's perspective is that when markets rate soften, obviously new borrowers will not borrow at the same rate as earlier. So if the base rate is fixed at 8%, and bank lends to corporates at Base Rate (8%) and possibly even to existing home loans seekers at Base Rates (8%). When interest rates in the market soften, the banks will be forced to reduce their Base rates as now new customers will not borrow at 8% and banks cannot lend below that rate without reducing their Base Rates. Thus banks will be forced to lower its base rate in response to market forces. Any reduction in base rates, will automatically apply to the old customer as well as new customers without any discrimination. . Domestic Term Deposits: The first one in the list is interest rates for domestic term depositsbelow one crore rupees. Tenors Existing w.e.f. 03.01.2011 7 days to 14 days 4.00 15 days to 45 days 5.00 46 days to 90 days 5.50 91 days to 180 days 6.00 181 days to less than 1 year 7.75 1 year to 554 days 8.25 555 days 9.00 556 days to less than 2 8.25 years 2 years to 999 days 8.75 1000 days 9.00 1001days to less than 3 8.75 years 3 year to less than 5 years 8.25 5 years to less than 8 years 8.50 8 years and up to 10 years 8.75
Revised w.e.f. 14.02.2011 7 days to 14 days 4.00 15 days to 45 days 5.00 46 days to 90 days 5.50 91 days to 180 days 6.00 181 days to less than 1 year 7.75 1 year to 554 days 8.25 555 days 9.25 8.25 556 days to less than 2 years 2 years to 999 days 8.75 1000 days 9.25 1001days to less than 3 8.75 years 3 year to less than 5 years 8.25 5 years to less than 8 years 8.50 8 years and up to 10 years 8.75
Here is the table that has those rates. 2. Domestic Term Deposits for more than one crore rupees: If you have more than a crore to spare for a term deposit – you will get a different interest rate. Here is that table: Tenors Revised w.e.f. 07.12.2010 7 days to 14 days 6.25 15 days to 30 days 6.25
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31 days to 45days 46 days to 90 days 91 days to 180 days 181 days to 270 days 271 days to less than 1 year 1 year to less than 2 years 2 years and above
6.50 7.00 7.25 7.75 8.00 8.50 8.00
3. Resident Indian Senior Citizens: Senior citizens get a slightly interest rate in India, but not if their deposit is more than a crore. Here is a table that shows these rates: Tenors Existing Revised w.e.f. w.e.f. 14.02.2011 03.01.2011 7 days to 14 days 4.00 7 days to 14 days 4.00 15 days to 45 days 5.00 15 days to 45 days 5.00 46 days to 90 days 5.50 46 days to 90 days 5.50 91 days to 180 days 6.00 91 days to 180 days 6.00 181 days to less 7.75 181 days to less than 1 7.75 than 1 year year 1 year to 554 days 8.75 1 year to 554 days 8.75 555 days 9.50 555 days 9.75 556 days to less 556 days to less than 2 8.75 8.75 than 2 years years 2 years to 999 days 9.25 2 years to 999 days 9.25 1000 days 9.50 1000 days 9.75 1001 days to less 1001days to less than 3 9.25 9.25 than 3 years years 3 year to less than 5 8.75 3 year to less than 5 8.75 years years 5 years to less than 5 years to less than 8 9.00 9.00 8 years years 8 years and up to 10 8 years and up to 10 9.25 9.25 years years 4. SBI staff and pensioners: If you are a SBI employee or pensioner – you will get 1% extra on top of the regular interest rate. If you are a pensioner above 60 years old, then you will get dual benefit – 0.50% extra for senior citizens, and 1% extra for the staff. 5. Savings Bank Interest Rates: Savings account get an interest rate of 3.5%. Let me know if I missed out anything or if you have any other questions, and also look at thefixed deposit rates in India offered by other banks. If you are a NRI, then the NRI Interest Rates page will be more meaningful for you, and if you are looking for more information on fixed deposits, then this page lists down more resources on fixed deposits. Origin
Punjab under the British especially after annexation in 1849 witnessed a period of rapid development giving rise to a new educated class fired with a desire for freedom from the yoke of slavery. Amongst the cherished desires of this new class was also an overriding ambition to start a Swadeshi Bank with Indian Capital and management representing all sections of the Indian community. The idea was first mooted by Rai Mool Raj of Arya Samaj who, as reported by Lal Lajpat Rai, had long cherished the idea that Indians should have a national bank of their own. He felt keenly "the fact that the Indian capital was being used to run English banks and companies,
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the profits accruing from which went entirely to the Britishers whilst Indians had to contend themselves with a small interest on their own capital". At the instance of Rai Mool Raj, Lala Lajpat Rai sent round a circular to selected friends insisting on an Indian Joint Stock Bank as the first special step in constructive Swadeshi. Lala Harkrishan Lal who had returned from England with ideas regarding commerce and industry, was eager to give them practical shape. On May 23, 1894, the efforts materialized. The founding board was drawn from different parts of India professing different faiths and a varied back-ground with, however, the common objective of providing country with a truly national bank which would further the economic interest of the country. The Bank opened for business on 12 April, 1895. The first Board of 7 Directors comprised of Sardar Dayal Singh Majithia, who was also the founder of Dayal Singh College and the Tribune; Lala Lalchand one of the founders of DAV College and President of its Management Society; Kali Prosanna Roy, eminent Bengali pleader who was also the Chairman of the Reception committee of the Indian National Congress at its Lahore session in 1900; Lala Harkishan Lal who became widely known as the first industrialist of Punjab; EC Jessawala, a well known Parsi merchant and partner of Jamshedji & Co. of Lahore; Lala Prabhu Dayal, a leading Rais, merchant and philanthropist of Multan; Bakshi Jaishi Ram, an eminent Civil Lawyer of Lahore; and Lala Dholan Dass, a great banker, merchant and Rais of Amritsar. Thus a Bengali, Parsi, a Sikh and a few Hindus joined hands in a purely national and cosmopolitan spirit to found this Bank which opened its doors to the public on 12th of April 1895. They went about it with a Missionary Zeal. Sh. Dayal Singh Majithia was the first Chairman, Lala Harkishan Lal, the first secretary to the Board and Shri Bulaki Ram Shastri Barrister at Lahore, was appointed Manager. A Maiden Dividend of 4% was declared after only 7 months of operation. Lala Lajpat Rai was the first to open an account with the bank which was housed in the building opposite the Arya Samaj Mandir in Anarkali in Lahore. His younger brother joined the Bank as a Manager. Authorised total capital of the Bank was Rs. 2 lakhs, the working capital was Rs. 20000. It had total staff strength of nine and the total monthly salary amounted to Rs. 320. The first branch outside Lahore was opened in Rawalpindi in 1900. The Bank made slow, but steady progress in the first decade of its existence. Lala Lajpat Rai joined the Board of Directors soon after. in 1913, the banking industry in India was hit by a severe crisis following the failure of the Peoples Bank of India founded by Lala Harkishan Lal. As many as 78 banks failed during this crisis. Punjab National Bank survived. Mr. JH Maynard, the then Financial Commissioner, Punjab, remarked...."Your Bank survived...no doubt due to good management". It spoke volumes for the measure of confidence reposed by the public in the Bank's management. The years 1926 to 1936 were turbulent and loss ridden ones for the banking industry the world over. The 1929 Wall Street crash plunged the world into a severe economic crisis. It was during this period that the Jalianwala Bagh Committee account was opened in the Bank, which in the decade that followed, was operated by Mahatma Gandhi and Pandit Jawaharlal Nehru. The five years from 1941 to 1946 were ones of unprecedented growth. From a modest base of 71, the number of branches increased to 278. Deposits grew from Rs. 10 crores to Rs. 62 crores. On March 31, 1947, the Bank officials decided to leave Lahore and transfer the registered office of the Bank to Delhi and permission for transfer was obtained from the Lahore High Court on June 20, 1947. PNB was then housed in the precincts of Sreeniwas in the salubrious Civil Lines, Delhi. Many a staff member fell victim to the widespread riots in the discharge of their duties. The conditions deteriorated further. The Bank was forced to close 92 offices in West Pakistan constituting 33 percent of the total number and having 40% of the total deposits. The Bank, however, continued to maintain a few caretaker branches. The Bank then embarked on its task of rehabilitating the displaced account holders. The migrants from Pakistan were repaid their deposits based upon whatever evidence they could produce. Such gestures cemented their trusts in the bank and PNB became a symbol of Trust and a name you can bank upon. Surplus staff posed a big problem. Fast expansion became a priority. The policy paid rich dividends by opening up an era of phenomenal growth. In 1951, the Bank took over the assets and liabilities of Bharat Bank Ltd. and became the second largest bank in the private sector. In 1962, it amalgamated the Indo-Commercial Bank with it. From its dwindled deposits of Rs. 43 crores in 1949 it rose to cross the Rs. 355 crores mark by the July 1969. Its number of offices had increased to 569 and advances from Rs. 19 crores in 1949 to Rs. 243 crores by July 1969 when it was nationalised. Since inception in 1895, PNB has always been a "People's bank" serving millions of people
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throughout the country and also had the proud distinction of serving great national leaders like Sarvshri Jawahar Lal Nehru, Gobind Ballabh Pant, Lal Bahadur Shastri, Rafi Ahmed Kidwai, Smt. Indira Gandhi etc. amongst other who banked with us.
Interest Rates - Deposit
Saving Account Interest Rates :
4.0 % p.a. (w.e.f. 3rd May 2011)
Domestic Term Deposit Interest Rates (% p.a.) w.e.f. 07.04.2011 Sl. No
Period
Below Rs. 1 Crore
Rs. 1 Cr. To Rs. 10 Cr.
1
7 to 14 days
4.00
4.00
2
15 to 45 days
4.50
4.50
3
46 to 60 Days
5.50
6.00
4
61 to 90 Days
5.50
7.50
5
91 to 179 days
7.00
8.00
6
180 days to 270 Days
8.00
8.50
7
271 days to less than 1 year
8.00
8.50
8
1 year
9.00
9.00
9
More than 1 year to 554 Days
9.00
8.75
10
555 Days
9.05
8.75
11
556 Days to < 2 years
9.00
8.75
12
2 years to 999 Days
9.00
8.50
13
1000 Days
9.15
8.50
14
1001 Days to < 3 years
9.00
8.50
15
3 years to 1110 Days
8.50
8.50
16
1111 Days
9.25
8.50
17
1112 Days to < 5 Years
8.50
8.50
18
5 years to 10 years
8.75
8.75
The rates of interest on Domestic Term Deposit of Senior Citizens will be 0.50% higher on all maturities (except Rs. 1 Crore to 10 Crores) as hitherto. These revised interest rates will be applicable to the fresh deposits and renewal of existing Term deposits. These interest rates would also apply to term deposit accounts opened under Capital Gains Account Scheme, 1988 (OPERATIVE IN ALL BRANCHES EXCEPT RURAL OFFICES). Interest Rates - Loans & Advances
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BPLR: 13.50% w.e.f. 05.05.2011 BASE RATE: 10.00% w.e.f. 05.05.2011 Interest Rate on Advances Linked to BPLR and Base Rate Interest Rate on Advances - Retail Segment Loan Home >> Interst Rates- Loans & Advances >> Corporate Rates
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LENDING RATES LINKED WITH BPLR AND BASE RATE BPLR - 13.00% (w.e.f. 01.02.2011) BASE RATE - 9.50% (w.e.f. 01.02.2011) Tenor premium of 0.50% is to be added for arriving at interest rate in respect of loans repayable in 3 years & above. 1. (A) Agricultural & Small Enterprises Advances (MSE) including Trading Advances covered under MSME Act BPLR System
Base Rate System
BPLR -0.75%
BR + 2.25%
BPLR
BR + 3.00%
iii) PNB Kalyani Card
BPLR -1.00%
BR + 2.00%
iv) Small Enterprises Advances (MSE)
BPLR -0.50%
BR + 2.50%
v) Small Entp. (micro entp.) @
BPLR -1.00%
BR + 2.00%
b) Advances over Rs. 50,000/- but upto Rs.2 lakh
BPLR
BR + 3.00%
c) Advances over Rs.2 lakh but upto Rs.20 lakh
BPLR
BR + 3.00%
As per credit risk rating
As per credit risk rating
a) Advances upto Rs. 50,000/1. Agricultural production credit ii) Agri. Term loans
d) Advances over Rs.20 lakh
Credit Risk Rating
BPLR System
Base Rate System
AAA
BPLR
BR + 3.25%
AA
BPLR + 0.50%
BR + 3.50%
A
BPLR + 1.00%
BR + 4.00%
BB
BPLR + 1.50% #
BR + 4.50% ##
B
BPLR + 2.00% #
BR + 5.00% ##
C
BPLR + 2.00% #
BR + 5.00% ##
D
BPLR + 2.00% #
BR + 5.00% ##
@ Advances to Micro Enterprises under SME category of borrowers enjoying fund based limits upto Rs. 25 lakh will be given concession of 1.00% in rate of interest. # Financing under Capital Investment Subsidy Scheme of National Horticulture Board for construction/ expansion/ modernization of cold storages and storages for horticulture produce, will continue @ BPLR + 1.00 for existing accs under BPLR system. ## Financing under Capital Investment Subsidy Scheme of National Horticulture Board for construction/expansion/modernization of cold storages and storages for horticulture produce, will continue @ Base Rate + 4.00% 1. (b) Trading Advances not covered under MSME Act
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Home >> Interst Rates- Loans & Advances >> Retail Rates
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BPLR - 13.00% (w.e.f. 01.02.2011) BASE RATE - 9.50% (w.e.f. 01.02.2011) LENDING RATE STRUCTURE FOR RETAIL SEGMENT Term Premium (TP) of 0.50% is to be added where specifically mentioned NO-1 Housing Finance to Individuals including NRIs / Flexible Housing scheme / Existing Fin Basket a/c
a) Housing Finance to Individuals including NRIs For repayment period
BPLR System
Base Rate System
Fixed Option
Fixed Option
Upto Rs 20 lac
Above Rs 20 lac
9.25%
10.00%
Above 5 & upto 10 yrs
9.00%
9.50%
BR+0.75% BR+1.50% BR+1.75%
Above 10 & upto 15 yrs
9.25%
9.75%
BR+0.75% BR+1.50% BR+1.75%
Above 15 & upto 20 yrs
9.25%
9.75%
BR+1.00% BR+1.75% BR+2.00%
Above 20 yrs & upto 25 yrs.
9.50%
10.00%
BR+1.00% BR+1.75% BR+2.00%
Upto 5 years Above 5 & upto 10 yrs Above 10 & upto 20 yrs Above 20 yrs & upto 25 yrs.
Upto 5 years
The fixed rates shall be fixed at rates, higher by a fixed spread as 10.00% 10.25% compared to that of floating rate of similar tenor and shall be made 10.50% 10.75% fixed for 5 years. At the time of 10.75% 11.00% each reset after 5 years, the fixed rate shall Floating be fixed Option at a rate, which Floating Option should be higher by the same Upto Rs 20 Above Rs 20 spread Uptoover Above 30 rate Rs. 75 the floating lac lac Rs30 lac onLacs to < ofLacs applicable the date resetand for 75 Lacs Above the original tenor. At present, the spread has been fixed at 50 bps. 8.75% 9.50% BR+0.50% BR+1.25% BR+1.50%
b) Flexible Housing (OD Component)
BPLR
BR+3.00%
c) OD Facility to Existing Housing Loan Borrowers for Personal Needs
BPLR
BR+3.00%
The aforesaid revised rates of interest under floating option will also be applicable in: Existing as well as new accounts in Flexi-Housing scheme (Term Loan component) In existing accounts in Fin Basket scheme which stands closed. The fixed rate of interest option of Housing Loans, disbursed on or after 01.08.2006, will be subject to reset Scheme clause of five years on all repayment tenors except tenor upto NO-2: Earnest Money Deposit 05 year. Extra 0.50% of Interest on card rate will be charged in a/cs in respect of 3rd or BPLR rate System Base Rate System subsequent house/flat.(as advised by RAMD (RBD) from time to time.) BPLR BR+3.00% • • •
•
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