SIMPLE INTEREST
MODULE OBJECTIVE Interest Interest is the cost of borrowing money. An interest rate is the cost stated as a percent of the amount borrowed per period of time, usually one year.
Simple Interest Simple interest is calculated on the original principal only. Accumulated interest from prior periods is not used in calculations for the following periods. Simple interest is normally used for a single period of less than a year, such as 30 or 60 days. Simple Interest = (P *R*T)/100
where: P = principal (original amount borrowed or loaned) R= interest rate for one period T = number of periods
IMPORTANT FORMULA
Principal: The money borrowed or lent out for a certain period is called the principal or the sum. Interest: Extra money paid for using other's money is called interest. Simple Interest (S.I.): If the interest on a sum borrowed for certain period is reckoned uniformly, then it is called simple interest. Let Principal = P, Rate = R% per annum (p.a.) and Time = T years. Then
PxRxT 100 100 x S.I. 100 x S.I. 100 x S.I. (ii). P = ;R= and T = . RxT PxT PxR (i). Simple Intereest =
SOLVED EXAMPLES 1. A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is: A.Rs. 650 B.Rs. 690 C.Rs. 698 D.Rs. 700 Answer: Option C Explanation: S.I. for 1 year = Rs. (854 - 815) = Rs. 39. S.I. for 3 years = Rs.(39 x 3) = Rs. 117. Principal = Rs. (815 - 117) = Rs. 698. 2. Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B? A.Rs. 6400 B.Rs. 6500 C.Rs. 7200 D.Rs. 7500 E. None of these
Answer: Option A Explanation: Let the sum invested in Scheme A be Rs. x and that in Scheme B be Rs. (13900 - x). Then,
x x 14 x 2 (13900 - x) x 11 x 2 + = 3508 100 100
28x - 22x = 350800 - (13900 x 22) 6x = 45000 x = 7500. So, sum invested in Scheme B = Rs. (13900 - 7500) = Rs. 6400.
3. A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum? A.Rs. 4462.50 B.Rs. 8032.50 C.Rs. 8900 D.Rs. 8925 E. None of these Answer: Option D Explanation: 100 x 4016.25 9x5 401625 = Rs. 45 = Rs. 8925. 4. How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest? A. 3.5 years B.4 years C. 4.5 years D.5 years Principal= Rs.
Answer: Option B Explanation: Time =
100 x 81 = 4 years. 450 x 4.5 years
5. Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest? A. 3.6 B.6 C. 18 D.Cannot be determined Answer: Option B Explanation: Let rate = R% and time = R years. Then,
1200 x R x R = 432 100
12R2 = 432 R2 = 36 R = 6. 6. A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest? A.3% B.4% C.5% D.6% E. None of these Answer: Option D Explanation: S.I. = Rs. (15500 - 12500) = Rs. 3000. Rate =
100 x 3000 = 6% 12500 x 4 %
7. A person takes a loan of Rs. 200 at 5% simple interest. He returns Rs. 100 at the end of 1 year. In order to clear his dues at the end of 2 years, he would pay: A.Rs. 105 B.Rs. 110 C.Rs. 115 D.Rs. 115.50 Answer: Option C Explanation: Amount to be paid
= Rs. 100 +
200 x 5 x 1 100 x 5 x 1 = Rs. 115. + 100 100
8. An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes: A.10% B.10.25% C.10.5% D.None of these Answer: Option B Explanation: Let the sum be Rs. 100. Then, 100 x 10 x 1 = Rs. 5 100 x 2 105 x 10 x 1 S.I. for last 6 months = Rs. = Rs. 5.25 100 x 2 S.I. for first 6 months = Rs.
So, amount at the end of 1 year = Rs. (100 + 5 + 5.25) = Rs. 110.25 Effective rate = (110.25 - 100) = 10.25% 9.A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is: A.5% B.7% 1 C.7 % D.10% 8 Answer: Option D Explanation: Let the rate be R% p.a. Then,
5000 x R x 2 3000 x R x 4 + = 2200. 100 100
100R + 120R = 2200 R=
2200 = 10. 220
Rate = 10%.
10.A sum of Rs. 725 is lent in the beginning of a year at a certain rate of interest. After 8 months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At the end of the year, Rs. 33.50 is earned as interest from both the loans. What was the original rate of interest? A.3.6% B.4.5% C.5% D.6% E. None of these Answer: Option E Explanation: Let the original rate be R%. Then, new rate = (2R)%. Note: Here, original rate is for 1 year(s); the new rate is for only 4 months i.e.
year(s).
725 x R x 1 362.50 x 2R x 1 + = 33.50 100 100 x 3 (2175 + 725) R = 33.50 x 100 x 3 (2175 + 725) R = 10050 (2900)R = 10050 10050 R= = 3.46 2900 Original rate = 3.46% 11. A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was: A.Rs. 2000 B.Rs. 10,000 C.Rs. 15,000 D.Rs. 20,000 Answer: Option C Explanation: Principal = Rs.
100 x 5400 = Rs. 15000. 12 x 3
12. A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is: A.5% B.8% C.12% D.15% Answer: Option C Explanation: S.I. for 3 years = Rs. (12005 - 9800) = Rs. 2205. S.I. for 5 years = Rs.
2205 x 5 = Rs. 3675 3
Principal = Rs. (9800 - 3675) = Rs. 6125. Hence, rate =
100 x 3675 = 12% 6125 x 5 %
13. What will be the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 years? A.1 : 3 B.1 : 4 C.2 : 3 D.Data inadequate E. None of these Answer: Option C Explanation: Let the principal be P and rate of interest be R%. PxRx6 6PR 6 100 Required ratio = = = = 2 : 3. PxRx9 9PR 9 100 14. A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned? A.Rs. 35 B.Rs. 245 C.Rs. 350 D.Cannot be determined E. None of these Answer: Option D Explanation: We need to know the S.I., principal and time to find the rate.
Since the principal is not given, so data is inadequate. 15. A person borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6 A.Rs. 112.50 C.Rs. 150
p.a for 2 years. Find his gain in the transaction per year. B.Rs. 125 D.Rs. 167.50
Answer: Option A Explanation: 25 2 5000 x 4 x 2 5000 x x 4 100 100 = Rs. (625 - 400) = Rs. 225. 225 Gain in 1 year = Rs. = Rs. 112.50 2
Gain in 2 years= Rs.
16.A father left a will of Rs.35 lakhs between his two daughters aged 8.5 and 16 such that they may get equal amounts when each of them reach the age of 21 years. The original amount of Rs.35 lakhs has been instructed to be invested at 10% p.a. simple interest. How much did the elder daughter get at the time of the will? (A) Rs. 17.5 lakhs (B) Rs. 21 lakhs (C) Rs. 15 lakhs (4D Rs. 20 lakhs Answer – Option (B) Solution: Let Rs.x be the amount that the elder daughter got at the time of the will. Therefore, the younger daughter got (3,500,000 - x). The elder daughter’s money earns interest for (21 - 16) = 5 years @ 10% p.a simple interest The younger daughter’s money earns interest for (21 - 8.5) = 12.5 years @ 10% p.a simple interest. As the sum of money that each of the daughters get when they are 21 is the same,
x+
= (3,500,000 - x) +
=> x +
= 3,500,000 - x +
=> 2x +
= 3,500,000 (1 +
-
)
=> = (3,500,000) => x = 2,100,000 = 21 lakhs.
DATA SUFFICIENCY PROBLEMS DIRECTION TO USE Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is / are sufficient to answer the given question. Read the both statements and
Give answer (A) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question. Give answer (B) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question. Give answer (C) if the data either in Statement I or in Statement II alone are sufficient to answer the question. Give answer (D) if the data even in both Statements I and II together are not sufficient to answer the question. Give answer(E) if the data in both Statements I and II together are necessary to answer the question.
1. The simple interest on a sum of money is Rs. 50. What is the sum? I. The interest rate is 10% p.a. II. The sum earned simple interest in 10 years. A.I alone sufficient while II alone not sufficient to answer B.II alone sufficient while I alone not sufficient to answer C.Either I or II alone sufficient to answer D.Both I and II are not sufficient to answer E. Both I and II are necessary to answer Answer: Option E Explanation: Given : S.I. = Rs. 50. I gives, R = 10% p.a.
II gives, T = 10 years. Sum =
100 x S.I. 100 x 50 = Rs. = Rs. 50. TxR 10 x 10
Thus, I and II together give the answer. 2. What is the sum which earned interest? I. The total simple interest was Rs. 7000 after 7 years. II. The total of sum and simple interest was double of the sum after 5 years. A.I alone sufficient while II alone not sufficient to answer B.II alone sufficient while I alone not sufficient to answer C.Either I or II alone sufficient to answer D.Both I and II are not sufficient to answer E. Both I and II are necessary to answer Answer: Option E Explanation: Let the sum be Rs. x. I gives, S.I. = Rs. 7000 and T = 7 years. II gives, Sum + S.I. for 5 years = 2 x Sum Now, S.I. for 7 years = Rs. 7000. S.I. for 1 year = Rs.
7000 = Rs. 1000. 7
Thus, I and II both are needed to get the answer. Correct answer is (E). .
Sum = S.I. for 5 years.
EXERCISE PROBLEM . Ex.l Find: S.l. on Rs 68000 at 16 2/3 % per annum for 9 months. Sol. P = 68000, R = 50/3 % p.a.
& T = 9/12 year = 3/4 years.
.. S.I. = ( PxRxT/100) = Rs. [6800 x 50/3 x ¾ x 1/100] = Rs. 8500 Ex.2 Find: S.l. on Rs 6250 at 14% per annum for 146 days. Sol. P = Rs. 6250,
R = 14 % p.a. & T = (146/365) year = 2/5 year .
:. S.l. = Rs (6250 x 14 x 2/5 x 1/100)= Rs 350. Ex.3 Find: S.l. on Rs 3000 at 18% per annum for the period from 4th Sol. Time = (24 + 31 + 18) days = 73 days = 1/5 year . P = Rs 3000 and R = 18 % p.a. :. S.I. = Rs (3000 x 18 x 1/5 x 1/100)= Rs 108 . Remark: The day on which money is deposited is not counted while the day on which money is withdrawn is counted. Ex. 4. A sum at simple interest at 13 i % per annum amounts to Rs. 2502.50 after 4 years. Find the sum. Sol. Let sum be x. Then S.I. = (X x 27/2 x 4 x 1/100) = 27X/50
.. Amount = ( X + 27X/50) = 77X/50 .. 77X/50 = 2502.50
or X= (2502.50 X 50)/77 = 1625
Hence Sum = Rs.1625 Ex. 5. A certain sum of money amounts to Rs 1008 in 2 years and to Rs 1164 in 3 i years. Find the sum and (be rate of interest. Sol. S.I. for 1 ½ years = Rs (1164 - 1008) = Rs 156 . S.I. for 2 years = Rs (156 x 2/3 x 2)= Rs 208. :. Principal = Rs (1008 - 208) = Rs 800. Now, P = 800, T= 2 and S.I. = 208. .. Rate = (100 x S.I.) / (P x T) =[ (100x208)/(800x2)]% =13% Ex.6. At what rate percent per annum will a sum of money double in 8 years Sol. Let principal = P, Then, S.I.=P and Time=8 years .. Rate = [(100 x P)/ (P x 8)]% = 12.5% per annum.. Ex. 7. A sum was put at simple interest at a certain rate for 3 years. Had it been put at 2% higher rate, it would have fetched Rs 360 more. Find the sum. Sol. Let, sum = P and original rate = R. Then, Px (R+2}x 3 100
P xRx 3 = 360 100
or 3PR + 6P - 3PR = 36000 or 6P = 36000 or P = 6000 . Hence, sum = Rs 6000 . Ex. 8. Simple interest on a certain sum is 16/25 of the sum. Find the rate percent and time, If both are numerically equal. Sol. Let sum = x. Then, S.I. = 16x / 25 Let rate = R % and time = R years. .. ( X x R x R)/(100) = 16x/25
or R2 =1600/25 R= 40/5 =8
:. Rate = 8% and Time = 8 years. Ex. 9. A man borrowed Rs 24000 from two money lenders. For one loan, he paid 15% per annum and for the other 18% per annum. At the end of one year, he paid Rs 4050. How much did he borrow at each rate ? Sol. Let the sum at 15% be Rs x and that at 18% be Rs (24000 - x). .. {(X x 15 x 1)/100 + {[(2400 – x) X 18 X 1]/100} = 4050 or 15 x + 432000 - 18x = 405000
or x = 9000.
:. Money borrowed at 15% = Rs 9000 . Money borrowed at 18% = Rs 15000.
Ex. 10. What annual instalment wiU discharge a debt of Rs 1092 due in 3 years at 12% simple interest? Sol. Let each instalment be Rs. x . then, { [x + (X x 12 x 2)/100] + [ X + (X + 12 x 2)/100] + x} =1092 or 28x/25 + 31x/25 +x=1092 or (28x+ 31x+25x) = (1092x25) or X= {(1092 x 25)/84} = 325 :. Each instalment = Rs. 325 Ex.11 A sum of money invested for a certain number of years at 8% p.a. simple interest grows to Rs.180. The same sum of money invested for the same number of years at 4% p.a. simple interest grows to Rs.120 only. For how many years was the sum invested?
Solution: From the information provided we know that, Principal + 8% p.a. interest on principal for n years = 180 …….. (1) Principal + 4% p.a. interest on principal for n years = 120 ……… (2) Subtracting equation (2) from equation (1), we get
4% p.a. interest on principal for n years = Rs.60. Now, we can substitute this value in equation (2), i.e Principal + 60 = 120 = Principal = Rs.60.
We know that SI = interest.
, where p is the principal, n the number of years and r the rate percent of
In equation (2), p = Rs.60, r = 4% p.a. and the simple interest = Rs.60.
Therefore, 60 = => n = 100/4 = 25 years. 12. How long will it take for a sum of money to grow from Rs.1250 to Rs.10,000, if it is invested at 12.5% p.a simple interest? Solution: Simple interest is given by the formula SI = (pnr/100), where p is the principal, n is the number of years for which it is invested, r is the rate of interest per annum In this case, Rs. 1250 has become Rs.10,000. Therefore, the interest earned = 10,000 – 1250 = 8750. 8750 = [(1250*n*12.5)/100] => n = 700 / 12.5 = 56 years.
DATA SUFFICIENCY PROBLEMS 1. What percentage of simple interest per annum did Anand pay to Deepak? I. Anand borrowed Rs. 8000 from Deepak for four years. II. Anand returned Rs. 8800 to Deepak at the end of two years and settled the loan.
A.I alone sufficient while II alone not sufficient to answer B.II alone sufficient while I alone not sufficient to answer C.Either I or II alone sufficient to answer D.Both I and II are not sufficient to answer E. Both I and II are necessary to answer
Answer: Option E Explanation: Let the rate be R% p.a. I gives, P = Rs. 8000 and T = 4 years. II gives, S.I. = Rs. (8800 - 8000) = Rs. 800. R=
100 x S.I. 100 x 800 1 = = 2 % p.a. PxT 8000 x 4 % 2
Thus, I and II both are needed to get the answer. Correct answer is (E). 2. What is the rate of simple interest? I. The total interest earned was Rs. 4000. II. The sum was invested for 4 years. A.I alone sufficient while II alone not sufficient to answer B. II alone sufficient while I alone not sufficient to answer C. Either I or II alone sufficient to answer D.Both I and II are not sufficient to answer E. Both I and II are necessary to answer Answer: Option D Explanation: We know that, R = 100 x S.I.
PxT Now, I gives, S.I. = Rs. 4000. II gives, T = 4 years. But, P is unknown. So, we cannot find R. So, given data is insufficient to get R. Correct answer is (D). 3. What is the principal sum? I. The sum amounts to Rs. 690 in 3 years at S.I. II. The sum amounts to Rs. 750 in 5 years at S.I. III. The rate of interest is 5% p.a. A.I and III only
B.II and III only C.I and II only D.I and III only, or II and III only E. Any two of the three
Answer: Option E Explanation: Clearly, any of the three will give us the answer. Correct answer is (E).
COMPOUND INTEREST
COMPOUND INTEREST Compound interest is calculated each period on the original principal and all interest accumulated during past periods. Although the interest may be stated as a yearly rate, the compounding periods can be yearly, semiannually, quarterly, or even continuously. IMPORTANT FORMULA Let Principal = P, Rate = R% per annum, Time = n years. When interest is compound Annually: Amount = P 1 +
R n 100
When interest is compounded Half-yearly: Amount = P 1 +
(R/2) 2n 100
When interest is compounded Quarterly: Amount = P 1 +
(R/4) 4n 100
When interest is compounded Annually but time is in fraction, say 3
Amount = P 1 +
years.
R
3x 1 + R 100 100
When Rates are different for different years, say R1%, R2%, R3% for 1st, 2nd and 3rd year respectively. Then, Amount = P 1 +
R1 100
R 1+ 2 100
R 1+ 3 . 100
Present worth of Rs. x due n years hence is given by: x Present Worth =
1+
R . 100
SOLVED EXAMPLE 1.
Find compound interest on Rs. 7500 at 4% per annum for 2 years, compounded annually. A. Rs.512
B. Rs.552
C. Rs.612
D. Rs.622
Solution = Rs[7500x(1+4/100)²] Amount =Rs.(7500x26/25x26/25) = Rs.8112. = Rs(8112 - 7500) C.I =Rs.612.
2.
Find the compound interest on Rs.16,000 at 20% per annum for 9 months, compounded quartely. A. Rs. 2552
B. Rs. 2512
C. Rs. 2572
D. Rs. 2592
Solution Principal
= Rs.16,000;
Time=9 months
= 3 quarters;
Amount =[16000x21/20x21/20x21/20] =Rs.[16000x(1+5/100)³] = Rs.18522. = Rs.(18522 - 16000) C.I = Rs.2522.
Simple interest on a certain sum of money for 3 years at 8% per annum is half the 3. compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is A. Rs. 1550
B. Rs. 1650
C. Rs. 1750
D. Rs. 2000
Solution C.I.
=Rs[4000x(1+10/100)²-4000]
Rs.(4000x11/10x11/10-4000) = Rs.940. =Rs. [420x100 /3x8] Sum = Rs.1750.
4.
Albert invested an amount of Rs.8000 in a fixed deposit scheme for 2 years at compound interest rate 5 p.c.p.a. How much amount will Albert get on maturity of the fixed deposit ? A. Rs. 8600
B. Rs. 8620
C. Rs. 8840
D. Rs. 8820
Solution =Rs.[8000x(1+5/100)² ] Amount = Rs. [8000 x 21/20x21/20] = Rs.8820.
5. The present worth of Rs.169 due in 2 years at 4% per annum compound interest is A. Rs.150.50
B. Rs.154.75
C. Rs.156.25
D. Rs.158
Solution = Rs.[169/(1+4/100)²] Present Worth = Rs.(169x25/26x25/26) = Rs.156.25
On a sum of money, the simple interest for 2 years is Rs. 660,while the compound 6. interest is Rs.696.30,the rate of interest being the same in both the cases. The rate of interest is A. 10%
B. 11%
C. 12%
D. 10.5%
Solution = Rs(696.30-660) Difference in C.I and S.I for 2 years =Rs. 36.30. S.I for one years S.I on Rs.330 for 1 year
= Rs330. =Rs. 36.30 = (100x36.30/330x1)%
Rate =11%. 7.
The difference between simple interest and compound interest on Rs. 1200 for one year at 10% per annum reckoned half yearly is A. Rs.2.50
B. Rs. 3
C. Rs. 4
D. Rs. 3.75
Solution = Rs.(1200x10x1/100) S.I Rs.120. =Rs[(1200x1+5/100)² -1200] C.I Rs.123. = Rs.[123-120] Difference Rs. 3.
8.
A sum of money invested at compound interest amounts to Rs. 800 in 3 years and to Rs. 840 in 4 years. The rate of interest per annum is A. 2x1/2%
B. 4%
C. 5%
D. 6x2/3%
Solution =Rs[840 - 800] S.I. on Rs.800 for 1 year = Rs.40 =(100x40/800x1)% Rate = 5%
9.
If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same at the same rate and for the same time? A. Rs. 51.25
B. Rs. 52
C. Rs. 54.25
D. Rs. 60
Solution Sum
=Rs.(50 x 100/2x5)
= Rs. 500. =[Rs.(500 x(1+5/100)²] Amount = Rs(500x21/20x21/20). =Rs. 551.25 = Rs. (551.25 - 500) C.I = Rs. 51.25
10.
In what time will Rs.1000 become Rs.1331 at 10% per annum compounded annually? A. 2 years
B. 3 years
C. 4 years
D. 7 years
Solution Principal
= Rs.1000;
Amount
= Rs.1331;
Rate
= Rs.10%p.a.
[1000(1+10/100)Λn;] Let the time be n years.Then = 1331. = (1331/1000) = (11/10)³ Therefore n = 3 years.
11.
If the simple interest on a sum of money at 5% per annum for 3 years is Rs. 1200, find the compound interest on the same sum for the same period at the same rate. A. 1251
B. 1261
C. 1271
D. 1281
Solution Clearly, Rate = 5% p.a ., Time
= 3 years
S.I
=Rs.1200. =Rs.(100 x 1200/3x5)
So,Principal =Rs.8000. =Rs.[8000 x (1+5/100)³] Amount
=Rs(8000x21/20x21/20x21/20) = Rs.9261 =Rs.(9261-8000)
C.I =Rs.1261. 12.
What will be the compound interest on a sum of Rs.25,000 after 3 years at the rate of 12 p.c.p.a? A. Rs.9000.30
B. Rs. 9720
C. Rs. 10123.20
D. Rs. 10483.20
Solution = Rs.(25000x(1+12/100)³ Amount =Rs.(25000x28/25x28/25x28/25) = Rs. 35123.20. C.I
=Rs(35123.20-25000)
=Rs.10123.20. 13.
The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is A. 2
B. 2½
C. 3
D. 4
Solution =Rs(30000 + 4347) Amount = Rs.34347. Let the time be n years.
= 34347. =34347/3000 Then, 30000(1+7/100)^n =11449/1000 =(107/100)^n n= 2years. 14. A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is: A.Rs. 120
B.Rs. 121
C.Rs. 122
D.Rs. 123
Answer: Option B Explanation: 5 5 2+ 1600 x 1 + 2 x 100 2 x 100 = Rs. 1600 x41x41+ 1600 x41
Amount= Rs. 1600 x 1 +
40 40 41 41 = Rs. 1600 x +1 40 40 1600 x 41 x 81 = Rs. 40 x 40 = Rs. 3321.
40
C.I. = Rs. (3321 - 3200) = Rs. 121 15. The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs.) is: A.625
B.630
C.640
D.650
Answer: Option A Explanation: Let the sum be Rs. x. Then, 4 676 51 2- x = x- x = x. 100 625 625 x x 4 x 2 2x S.I. = = . 100 25 51x 2x - =1 625 25 C.I. = x 1 +
x = 625 16. There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate? A.Rs. 2160
B.Rs. 3120
C.Rs. 3972
D.Rs. 6240
E.None of these
Answer: Option C Explanation:
Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years. R=
100 x 60 = 10% p.a. 100 x 6
Now, P = Rs. 12000. T = 3 years and R = 10% p.a. C.I.= Rs. 12000 x
1+
10 3- 1 100
331 = Rs. 12000 x 1000 = 3972. 17. What is the difference between the compound interests on Rs. 5000 for 1 annum compounded yearly and half-yearly? A.Rs. 2.04
B.Rs. 3.06
C.Rs. 4.80
D.Rs. 8.30
years at 4% per
Answer: Option A Explanation: C.I. when interest compounded yearly
4 = Rs. 5000 x 1 + x 1+ x4 100 100 26 51 = Rs. 5000 x x 25 50 = Rs. 5304. 2 C.I. when interest is = Rs. 5000 x 1 + 3 compounded half-yearly 100 51 51 51 = Rs. 5000 x x x 50 50 50 = Rs. 5306.04 Difference = Rs. (5306.04 - 5304) = Rs. 2.04 18. The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is: Answer: Option A Explanation:
Amount = Rs. (30000 + 4347) = Rs. 34347. Let the time be n years. 7 n= 34347 100 107 34347 11449 107 n= = = 2 100 30000 10000 100
Then, 30000 1 +
n = 2 years. 19. What will be the compound interest on a sum of Rs. 25,000 after 3 years at the rate of 12 p.c.p.a.? A.Rs. 9000.30
B.Rs. 9720
C.Rs. 10123.20
D.Rs. 10483.20
E.None of these
Answer: Option C Explanation: 12 3 100 28 28 28 = Rs. 25000 x x x 25 25 25 = Rs. 35123.20
Amount= Rs. 25000 x 1 +
C.I. = Rs. (35123.20 - 25000) = Rs. 10123.20 20. At what rate of compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2 years? A.6%
B.6.5%
C.7%
D.7.5%
Answer: Option A Explanation: Let the rate be R% p.a. Then, 1200 x 1 + R
2= 1348.32
100 R 134832 11236 1+ 2= = 100 120000 10000 R 106 1+ 2= 2 100 100 R 106 1+ = 100 100 R = 6%
DATA SUFFICIENCY PROBLEM Directions to Solve Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is / are sufficient to answer the given question. Read the both statements and
Give answer (A) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question. Give answer (B) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question. Give answer (C) if the data either in Statement I or in Statement II alone are sufficient to answer the question. Give answer (D) if the data even in both Statements I and II together are not sufficient to answer the question. Give answer(E) if the data in both Statements I and II together are necessary to answer the question.
1. What is the rate of compound interest? I. The principal was invested for 4 years. II. The earned interest was Rs. 1491. A.I alone sufficient while II alone not sufficient to answer B.II alone sufficient while I alone not sufficient to answer C.Either I or II alone sufficient to answer D.Both I and II are not sufficient to answer E. Both I and II are necessary to answer Answer: Option D Explanation: Let Principal = Rs. P and Rate = R% p.a. Then,
Amount = Rs. P 1 +
R 4 100
R 1+ 4- 1 100 R 1+ 4- 1 = 1491. 100
C.I. =P P
Clearly, it does not give the answer. Correct answer is (E). 2. What will be compounded amount? I. Rs. 200 was borrowed for 192 months at 6% compounded annually. II. Rs. 200 was borrowed for 16 years at 6%. A.I alone sufficient while II alone not sufficient to answer B.II alone sufficient while I alone not sufficient to answer C.Either I or II alone sufficient to answer D.Both I and II are not sufficient to answer E. Both I and II are necessary to answ Answer: Option C Explanation: 6 I. Amount = Rs. 200 x 1 + 16 100 6 II. Amount = Rs. 200 x 1 + 16 100 Thus, I as well as II gives the answer. Correct answer is (C).
EXERCISE PROBLEMS 1. The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is: A.3
B.4
C.5
D.6
Answer: Option B Explanation: 20 n> 2P 100 6 6 6 6 Now, x x x > 2. 5 5 5 5 P 1+
6 n> 2. 5
So, n = 4 years.
2. Albert invested an amount of Rs. 8000 in a fixed deposit scheme for 2 years at compound interest rate 5 p.c.p.a. How much amount will Albert get on maturity of the fixed deposit? A.Rs. 8600
B.Rs. 8620
C.Rs. 8820
D.None of these
Answer: Option C Explanation: 5 2 100 21 21 = Rs. 8000 x x 20 20 = Rs. 8820.
Amount= Rs. 8000 x 1 +
3. The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is: A.6.06%
B.6.07%
C.6.08%
D.6.09%
Answer: Option D Explanation: 3 Amount of Rs. 100 for 1 year = Rs. 100 x 1 + 2 = Rs. 106.09 when compounded half-yearly 100 Effective rate = (106.09 - 100)% = 6.09% 4. Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is: A.Rs. 1550
B.Rs. 1650
C.Rs. 1750
D.Rs. 2000
Answer: Option C
Explanation: 10 2- 4000 100 11 11 = Rs. 4000 x x - 4000 10 10 = Rs. 840. 420 x 100 Sum = Rs. = Rs. 1750. 3x8
C.I.= Rs. 4000 x 1 +
5. If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same at the same rate and for the same time? A.Rs. 51.25
B.Rs. 52
C.Rs. 54.25
D.Rs. 60
Answer: Option A Explanation: Sum = Rs.
50 x 100 = Rs. 500. 2x5
5 2 100 21 21 = Rs. 500 x x 20 20 = Rs. 551.25
Amount= Rs. 500 x 1 +
C.I. = Rs. (551.25 - 500) = Rs. 51.25 6.The difference between simple interest and compound on Rs. 1200 for one year at 10% per annum reckoned half-yearly is: A.Rs. 2.50
B.Rs. 3
C.Rs. 3.75
D.Rs. 4
E.None of these
Answer: Option B Explanation: 1200 x 10 x 1 = Rs. 120. 100 5 C.I. = Rs. 1200 x 1 + 2- 1200 = Rs. 123. 100 S.I. = Rs
Difference = Rs. (123 - 120) = Rs. 3. 7. The difference between compound interest and simple interest on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum? A.8
B.10
C.12
D.Cannot be determined
E.None of these
Answer: Option A Explanation: R 15000 x R x 2 15000 x 1 + 2- 15000 = 96 100 100 R 2R =15000 1 + 2- 1 = 96 100 100
(100 + R)2 - 10000 - (200 x R) = 96 10000 96 x 2 R2 = = 64 3 15000
R = 8. Rate = 8%. 8. The compound interest on a certain sum for 2 years at 10% per annum is Rs. 525. The simple interest on the same sum for double the time at half the rate percent per annum is: A.Rs. 400
B.Rs. 500
C.Rs. 600
D.Rs. 800
Answer: Option B Explanation: Let the sum be Rs. P. 10 Then, P 1 + 2- P = 525 100 11 P 2- 1 = 525 10 525 x 100 P= = 2500. 21 Sum = Rs . 2500. So, S.I. = Rs.
2500 x 5 x 4 = Rs. 500 100
9. What will Rs.1500 amount to in three years if it is invested in 20% p.a. compound interest, interest being compounded annually? (A) 2400 (B) 2592 (C) 2678 (D) 2540 Answer -Option (B) Solution: The usual way to find the compound interest is given by the formula A = In this formula, A is the amount at the end of the period of investment
.
P is the principal that is invested r is the rate of interest in % p.a And n is the number of years for which the principal has been invested.
In this case, it would turn out to be A = = 2592. 10. If a sum of money grows to 144/121 times when invested for two years in a scheme where interest is compounded annually, how long will the same sum of money take to treble if invested at the same rate of interest in a scheme where interest is computed using simple interest method? (A) 9 years (B) 22 years Answer - Option(B)
(C) 18 years
(D) 33 years
Solution The sum of money grows to
times in 2 years.
If P is the principal invested, then it has grown to interest.
P in two years when invested in compound
In compound interest, if a sum is invested for two years, the amount is found using the following formula = =>
P in this case. =>
=>
=>
If r = , then in simple interest the time it will take for a sum of money to treble is found out as follows: Let P be the principal invested. Therefore, if the principal trebles = 3P, the remaining 2P has come on account of simple interest.
Simple Interest = , where P is the simple interest, r is the rate of interest and ‘n’ is the number of years the principal was invested.
Therefore, 2P =
=> 2 =
or n = 22 years.
11.The population of a town was 3600 three years back. It is 4800 right now. What will be the population three years down the line, if the rate of growth of population has been constant over the years and has been compounding annually? (A) 6000 (B) 6400 (C) 7200 (D) 9600 Answer - Option(B) Solution: The population grew from 3600 to 4800 in 3 years. That is a growth of 1200 on 3600 during three year span.
Therefore, the rate of growth for three years has been The rate of growth during the next three years will also be the same. Therefore, the population will grow from 4800 by = 1600 Hence, the population three years from now will be 4800 + 1600 = 6400 12. A man invests Rs.5000 for 3 years at 5% p.a. compound interest reckoned yearly. Income tax at the rate of 20% on the interest earned is deducted at the end of each year. Find the amount at the end of the third year. (A) 5624.32 (B) 5630.50 Answer – Option (A)
(C) 5788.125
(D) 5627.20
Solution: 5% is the rate of interest. 20% of the interest amount is paid as tax. That is 80% of the interest amount stays back. Therefore, if we compute the rate of interest as 80% of 5% = 4% p.a., we will get the same value. The interest accrued for 3 years in compound interest = 3*simple interest on principal + 3*interest on simple interest + 1*interest on interest on interest. = 3*(200) + 3*(8) + 1*0.32 = 600 + 24 + 0.32 = 624.32 The amount at the end of 3 years = 5000 + 624.32 = 5624.32 13. The difference between the compound interest and the simple interest on a certain sum at 12% p.a. for two years is Rs.90. What will be the value of the amount at the end of 3 years? (A) 9000 (B) 6250 Answer –Option (D)
(C) 8530.80
(D) 8780.80
Solution: , when interest is reckoned using compound interest, interest being compounded annually. The difference in the simple interest and compound interest for two years is on account of the interest paid on the first year's interest Hence 12% of simple interest = 90 => simple interest =
=750.
As the simple interest for a year = 750 @ 12% p.a., the principal =
= Rs.6250.
If the principal is 6250, then the amount outstanding at the end of 3 years = 6250 + 3(simple interest on 6250) + 3 (interest on simple interest) + 1 (interest on interest on interest) = 6250 + 3(750) + 3(90) + 1(10.80) = 8780.80. 14. Rs. 5887 is divided between Shyam and Ram, such that Shyam's share at the end of 9 years is equal to Ram's share at the end of 11 years, compounded annually at the rate of 5%. Find the share of Shyam. (A) 2088
(B) 2000
(C) 3087 (D) None of these Answer –Option (C) Solution: Shyam's share * (1+0.05)9 = Ram's share * (1 + 0.05)11 Shyam's share / Ram's share = (1 + 0.05)11 / (1+ 0.05)9 = (1+ 0.05)2 = 441/400 Therefore Shyam's share = (441/841) * 5887 = 3087. 15. The question for the day is from the topic simple and compound interest. Shawn
invested one half of his savings in a bond that paid simple interest for 2 years and received Rs.550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received Rs.605 as interest. What was the value of his total savings before investing in these two bonds? (A) Rs.5500
(B) Rs.11000
(C) Rs.22000 (D) Rs.2750 Answer - Option (D) Solution: Shawn received an extra amount of (Rs.605 – Rs.550) Rs.55 on his compound interest paying
bond as the interest that he received in the first year also earned interest in the second year. The extra interest earned on the compound interest bond = Rs.55 The interest for the first year =
Therefore, the rate of interest =
= Rs.275
= 20% p.a.
20% interest means that Shawn received 20% of the amount he invested in the bonds as interest. If 20% of his investment in one of the bonds = Rs.275, then his total investment in each of the bonds =
= 1375.
As he invested equal sums in both the bonds, his total savings before investing = 2*1375 = Rs.2750. 16. Rs.100 doubled in 5 years when compounded annually. How many more years will it
take to get another Rs.200 compound interest? (A)10 years
(B) 5 years
(C) 7.5 years (D) 15 years
(E) 8 years
Answer - Option (B) Solution Rs.100 invested in compound interest becomes Rs.200 in 5 years. The amount will double again in another 5 years. i.e., the amount will become Rs.400 in another 5 years. So, to earn another Rs.200 interest, it will take another 5 years. Correct answer choice (2). 17. Find the effective rate of interest for an investment that earns 51 2% per year, compounded continuously. Solution: We are not given a value of P in this problem, so either pick a value for P and stick with that throughout the problem, or just let P = P. We have that t = 1, and r = .055. To find the effective rate of interest,
first find out how much money we have after one year: A = Pert A = Pe(.055)(1) A = 1.056541P. Therefore, after 1 year, whatever the principal was, we now have 1.056541P. Next, find out how much interest was earned, I, by subtracting the initial amount of money from the final amount: I=A−P = 1.056541P − P = .056541P. Finally, to find the effective rate of interest, use the simple interest formula, I = Prt. So, I = Pr(1) = .056541P .056541 = r. Therefore, the effective rate of interest is 5.65%.
DATA SUFFICIENCY PROBLEM 1. An amount of money was lent for 3 years. What will be the difference between the simple and the compound interest earned on it at the same rate? I. The rate of interest was 8 p.c.p.a. II. The total amount of simple interest was Rs. 1200. A.I alone sufficient while II alone not sufficient to answer B.II alone sufficient while I alone not sufficient to answer C.Either I or II alone sufficient to answer D.Both I and II are not sufficient to answer E. Both I and II are necessary to answer
Answer: Option E Explanation: Given: T = 3 years. I. gives: R = 8% p.a. II. gives: S.I. = Rs. 1200. Thus, P = Rs. 5000, R = 8% p.a. and T = 3 years.
Difference between C.I. and S.I. may be obtained. So, the correct answer is (E). 2.What will be the compound interest earned on an amount of Rs. 5000 in 2 years? I. The simple interest on the same amount at the same rate of interest in 5 years is Rs. 2000. II. The compound interest and the simple interest earned in one year is the same. III. The amount becomed more than double on compound interest in 10 years. A.I only
B.I and II only C.II and III only D.I and III only E. None of these
Answer: Option A Explanation: P = Rs. 5000 & T = 2 years. I. S.I. on Rs. 5000 in 5 years is Rs. 2000. 5000 x R x 5 = 2000 100
R = 8.
Thus I only gives the answer. Correct answer is (A). 3.What is the rate of interest p.c.p.a.? I. An amount doubles itself in 5 years on simple interest. II. Difference between the compound interest and the simple interest earned on a certain amount in 2 years is Rs. 400. III. Simple interest earned per annum is Rs. 2000. A.I only
B.II and III only C.All I, II and III D.Any two of the three
E. I only or II and III only
Answer: Option E Explanation: PxRx5 =P R = 20. 100 R PxRx2 II. P 1 + 2- P = 400 100 100 PxRx1 = 2000 PR = 200000. III. 100 PR2 4000000 = R = 20. PR 200000 I.
PR2 = 4000000.
Thus I only or (II and III) give answer. Correct answer is (E). 4. Mr. Gupta borrowed a sum of money on compound interest. What will be the amount to be repaid if he is repaying the entire amount at the end of 2 years? I. The rate of interest is 5 p.c.p.a. II. Simple interest fetched on the same amount in one year is Rs. 600. III. The amount borrowed is 10 times the simple interest in 2 years. A. I only B. III only C. I or II only D.II and Either I or III only
All I, II and III are required Answer: Option D Explanation: E. I. gives, Rate = 5% p.a.
II. gives, S.I. for 1 year = Rs. 600. III. gives, sum = 10 x (S.I. for 2 years). Now I, and II give the sum.
For this sum, C.I. and hence amount can be obtained. Thus, III is redundant. Again, II gives S.I. for 2 years = Rs. (600 x 2) = Rs. 1200. Now, from III, Sum = Rs. (10 x 1200) = Rs . 12000. Thus, Rate =
100 x 1200 = 5% p.a. 2 x 12000
Thus, C.I. for 2 years and therefore, amount can be obtained. Thus, I is redundant. Hence, I or III redundant. 5.What is the compound interest earned at the end of 3 years? I. Simple interest earned on that amount at the same rate and for the same period is Rs. 4500. II. The rate of interest is 10 p.c.p.a. III. Compound interest for 3 years is more than the simple interest for that period by Rs. 465. A.I and II only B.II and III only C.I and III only D.Either II or III only E. Any two of the three Answer: Option D Explanation: I. gives, S.I for 3 years = Rs. 4500. II. gives, Rate = 10% p.a. III. gives, (C.I.) - (S.I.) = Rs. 465. Clearly, using I and III we get C.I. = Rs. (465 + 4500). Thus, II is redundant.
Also, from I and II, we get sum =
100 x 4500 = 15000. 10 x 3
Now C.I. on Rs. 15000 at 10% p.a. for 3 years may be obtained. Thus, III is redundant. Either II or III is redundant.
