Level – I
1. You have deposited 1,00,000 in postal saving schemes, it provides 8.5% rate of return on deposits. Calculate the simple interest that will be earned a fter 5 years of maturity. 2. Mr. A deposits Rs. 50,000 in a nationalized bank which provides 9.5% return on its fixed deposits. Having maturity of 9 years and 6 months. Find out total amount received by Mr. A after maturity. 3. At the rate of 8.5% p.a. simple interest, a sum of Rs. 4,800 will earn how much interest in 2 years and 3 months?
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? 5. How much time will it take for an amount of Rs. 100 to yield Rs. 50 as interest at 10% p.a. of simple interest? 6. How much time will it take for an maount of Rs. 1,000 to yield Rs. 350 as interest at 12% p.a. of simple interest? 7. 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? 8. A sum of Rs. 5,000 amounts to Rs. 6,800 in 3 years at the rate of simple interest. What is the rate of interest? 9. A sum of Rs. 12,000 amounts to Rs. 24,000 in 5 years at the rate of simple interest. What is the rate of interest? 10. A man took a loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5,400 interest only for the period. The principal amount borrowed by him was. 11. If the simple interest of a loan amount to Rs. 5,100 taken for 3 years at the rate of 17% what would be the principle amount? 12. If the simple interest of a loan amount to Rs. 50 taken for 2 years at the rate of 5%. What would be the principal amount? 13. A sum at simple interest at 13.5% p.a. amounts to Rs. 2,502.50 after 4 years find the sum. 14. A sum at simple interest at 12% p.a. amounts to Rs. 160 after 5 years find the sum. 15. A sum at simple interest at 10% p.a. amounts to Rs. 2,750 after 5 years find the sum.
Level – II
1. Mr. R deposited Rs. 7,500 at 4% p.a. in a bank for 2 years, compounded annually. Calculate total amount after 2 years. 2. You deposit 1,000 today in a bank which pays 10% interest compounded annually, how much will the deposit grow to after 8 years and 12 years? 3. What will Rs. 10,000 amount to in 4 years, if interest rate is 10% p.a. compounded annually? 4. If we invest Rs. 50,000 in the bank where it earns 8% compounded annually. How much will it be worth at the end of 5 years? 5. Find out the future value v alue of 2,00,000 invested for 5 years at 15% rate of interest? 6. How many years will it take for initial investment of Rs. 10,000 to grow to Rs. 67,275 if it is invested at 10% compounded annually? 7. How many years will it take for initial investment of Rs. 20,000 to grow to Rs. 32,210 if it is invested at 10% compounded annually? 8. How many years will it take for initial investment of Rs. 5,000 to grow to Rs. 8,811 if it is invested at 12% compounded annually? 9. Someone promises to give you Rs. 5,000 after 8 years in exchange for Rs. 1,000 today. What interest rate is implicit in this offer?
1. Mr. A wants to purchase a car of Rs. 10,00,000 after 5 years. How much lump sum amount he should deposit in a bank giving 10% return on F.D in presents? 2. Mr. Z wants to purchase a house of 5,00,000 after 3 years. How much lump sum amount he should save in a bank that 12% return at present time? 3. A SSC student is planning to study in MBA programme. The programme fee is Rs. Rs. 2,50,000. How much he should save in a bank giving 7.5% return so as to pay fees after 5 years? 4. Mr. K is planning to invest funds (lump sum) for his daughter’s marriage after 15 years. Recently he won lottery prize of Rs. 25,00,000. He has estimated the cost of marriage function to be 75,00,000. But he doesn’t do esn’t know how much amount he should invest in a mutual fund scheme which has provided a return of o f 12% over the last 10 years. Help him out. 5. What would be the present value of Rs. 1,21,000 to be received in two years when discounted at 10%? 6. Find out present value of Rs. 10,000 receivable after 8 years if the rate of discount is (1) 10% (2) 12% and (3) 15%. 7. You have decided to deposit Rs. 30,000 per year in PPF for 30 years. What will be the accumulated amount in PPF at the end of 30 years if interest rate is 11%? 8. Compute the future values of (i) an initial Rs. 100 compounded annually for 10 years at 10 per cent (ii) an annuity of Rs. 100 for 10 years at 10 per cent. 9. Fifteen Annual payments of Rs. 5,000 are made into a deposit account that pays 14% per year. What is the future value of this annuity at a t the end of 15 years? 10. Suppose a firm deposits Rs. 5,000 5,0 00 at the end of each ea ch year for four years at 6% rate of interest. How much would this annuity accumulate at the end of the fourth year? 11. A four year annuity, of Rs. 3,000 per year is deposited in a bank account that pays 9% interest compounded annually. The annuity payments begin in year 12 from now. What is the future value of annuity? 12. You want to buy a house after 5 years when it is expected to cost Rs. 2 million. How much should you save annually if your savings earn a compound rate of 12%/ 13. How much must be deposited in an 10% saving A/c at the end of each year in order to accumulate Rs. 1,50,000 at the end of 10 years? 14. A person person would need Rs. 100 5 years from now. How much amount should he deposit each year in his bank account, if the yearly interest is 10 per cent?
15. Mr. Vinay plans to send his son for higher studies abroad after 10 years. He expects the cost of these studies to be Rs. 1,00,000. How much should he save annually to have a sum of Rs. 1,00,000 at the end of 10 years, if interest rate is 12%? 16. A Company has issued debentures of Rs. 50 lakh to be repaid after 7 years. How much should the company invest in a sinking fund earning 12 per cent in order to be able to repay debentures? 17. You want to take a world tour which costs Rs. 1,00,000 – the cost is expected to remain unchanged unchanged in nominal nominal terms. You are willing willing to save annually annually Rs. 80,000 to fulfill your desire. How long you will have to wait if your savings earn a return of 14% per annum? 18. You want to take a trip on the moon which costs Rs. 10,00,000 – the cost is expected to remain unchanged in nominal terms. You can save annually Rs. 50,000 to fulfill your desire. How long you will have to wait if your savings earn an interest of 12 per cent?
Level - III
1. A finance company advertises that it will pay a lump sum of Rs. 44, 650 at the end of five years to investors who deposit annually Rs. 6,000 for 5 years. What is the interest rate implicit in this offer? 2. A finance company advertises that it will pay a lump sum of Rs. 10,000 at the end of six years to investors who deposit annually Rs. 1,000. 1,000 . What is the interest rate implicit in this offer? 3. Mr. Z expects to receive Rs. 1,000 annually for 3 years, each receipt occurring at the end of each year. What is the present p resent value of this stream of benefits if the discount rate is 10 per cent? 4. After receiving your budget, you have determined that you can afford to pay Rs. 12,000 per month for 3 years towards a new car. You call finance company and learn that going rate of interest on car finance is 1.5 per cent per month for 36 months. How much you can borrow? 5. What is the present value of o f the following cash stream if the discount rate is 14 per cent? Year Cash flow
0 5,000
1 6,000
2 8,000
3 9,000
4 8,000
6. What is the present value of a 5 year annuity of Rs. 2,000 at 10%? 7. What is the rate present value of income stream which provides Rs. 1,000 at the end of year one, Rs. 2,500 at the end of year two, and Rs. 5,000 during each of the years 3 through 10, if the discount rate is 12%? 8. ABC Ltd has borrowed Rs. 1,000 to be repaid in equal instalments at the end of the next 3 years. The interest rate is 15%. Prepare loan amortization schedule. 9. Shyam borrows Rs. 80,000 for a musical system at a monthly interest of 1.25%. The loan is to be repaid in 12 equal monthly installments payable at the end of each month. Prepare loan amortization schedule. 10. You want to borrow Rs. 10,80,000 to buy a flat. You approach a housing finance company whic which h char charge gess 12.5 12.5 per per cent cent inte intere rest st.. You can can pay Rs. Rs. 1,80, 1,80,000 000 per per year year towa toward rd loan loan amortization. What would be the maturity period of loan? 11. Suppose someone offers you the following financial contract: if you deposit Rs. 10,000 with him he promises to pay Rs. 2,500 annually for 6 years. What interest rate do you earn on this deposit? 12. Suppose someone offers you the following financial contract: if you deposit Rs. 20,000 with him he promises to pay Rs. 4,000 annually for 10 years. What interest rate do you earn on this deposit?
Level - IV
1. Suppose a firm deposits Rs. 5,000 at the end of each year for four years at 6% rate of interest. How much would this annuity accumulate at the end of the fourth year? (FVIFA Ex. 10 Level-2) 2. Suppose a firm deposits Rs. 5,000 at the beginning of each year for four years at 6% rate of interest. How much would this annuity accumulate at the end of the fourth year? (FVIFA) 3. Mr. Z expects to receive Rs. 1,000 annually for 3 years, each receipt occurring at the end of each year. What is the present value of this stream of benefits if the discount rate is 10 per cent? (PVIFA – Ex.3 Level-2) 4. Mr. Z expects to receive Rs. 1,000 annually for 3 years, each receipt occurring at the beginning of each year . What is the present value of this stream of benefits if the discount rate is 10 per cent? 5. A person opens a recurring deposit account for a period of 10 years earning 12% interest and accepts the scheme under the condition that for the first year the deposit is Rs. 3,150 and for subsequent years the deposit amount will increase by b y 5% every year. What is the present value of this scheme? 6. A company paid a dividend of Rs. 120 last year. The dividend stream commencing one year is expected to grow at 10 per cent per annum for 15 years and then ends. If the discount rate is 21 per cent, what is the present value of the expected series? 7. An investor wants to know the present value of perpetuity of Rs. 10,000. If the interest rate is 10%. 8. Mr. X wishes to find out the present value of investments which yield Rs. 500 in perpetuity, discounted at 5%. 9. If someone promises to pay Rs. 1,000 each year in perpetuity, what is that promise worth of discount rate is 16%? 10. What is the present value of cash flows of Rs. 750 per year forever (a) at an interest rate of 8% and (b) at an interest rate of 10%? 11. An office complex is expected to generate a net rental of Rs. 3 million next year, which is expected to increase by 5% every year. If we assume that the increase will continue indefinitely, the rental stream is growing perpetuity. If the discount rate is 1 0% find out present value. 12. If the interest rate is 8%. Find out the doubling period. 13. If the interest rate is 4%. Find out the doubling period.
14. If the interest rate is 12%, what are the doubling periods as per the rule of 72 and the rule of 69 respectively? 15. If you deposit 5,000 today at 12% rate of interest in how many years (roughly) will this amount grow to Rs. 1,60,000? Work out this problem using rule of 72 – do not use tables. 16. Find out the future value of Rs. 1,000 at 12% interest compounded annually for 1 year. a. In above problem, find out future value if compounding is done d one semi-annually. 17. A borrower offers 16% nominal rate of interest with quarterly compounding. What is the effective rate of interest? 18. What is the difference between the effective rate of interest and stated rate of interest in the following cases: a. Stated rate of interest is 12% and the frequency of compounding is six times a year. b. Stated rate of interest is 24% and the frequency of compounding is four times a year. c. Stated rate of interest is 24% and the frequency of compounding is twelve times a year.
Level – V
1. Novelty Industries establishing a sinking fund to redeem Rs. 50,00,000 bond issue which matures in 15 years. How much do they have to put into the fund at the end of each year to accumulate 50,00,000 assuming the funds are compounded at 7% annually? 2. XYZ is creating a sinking fund to redeem its preference capital of Rs. 5 lakhs issued on January 1, 1998 and maturing on December 2009. The annual payment will start on January 1, 1998. The company will make equal payments and expects that the fund will earn 12% per year. How much will be the amount of sinking fund payment? 3. A company has issued debentures of Rs. 50 lakhs to be repaid after 7 years. How much should the company invest in sinking fund earning 12% in order to be able to repay debentures? 4. The XYZ company is establishing a sinking fund to retire Rs. 5,00,000 8% debentures 10 years from today. The company plans to put a fix amount into the fund, each year for 10 years. The first payment will be made at the end of current year. The company anticipates that the fund will earn 6% a year. What annual equal contributions must be made to accumulate Rs. 5,00,000, 10 years from now? 5. What is the present value of an income stream which provides Rs. 2,000 a year for the first five year and Rs. 3,000 a year forever, if the discount rate is 10%? 6. Mr. Raghu deposits 10,000 in a bank now. The interest rate is 10 per cent and compounding is done semi-annually. What will be the deposit grow to after 10 years? If the inflation rate is 8 per cent per year, what will be the value of deposit after 10 years of the current rupee? 7. As a winner of competition, you can choose one of the following prizes: 7.1. 5,00,000 now 7.2. 10,00,000 at the end of 6 years. 7.3. 60,000 a year forever 7.4. Rs. 1,00,000 per year for 10 years 7.5. Rs. 35,000 next year and rising thereafter by 5 per cent forever. 8. Assume that a deposit is to be made at year zero; into an account that earn 8% compounded annually. It is desired to withdraw Rs. 5,000 three years from now and Rs. 7,000 six year from now. What is the size of the year zero deposit that will produce these future payments. 9. A firm is due to receive Rs. 1,00,000 a year for next 5 years and Rs. 1,40,000 at the end of sixth year. Money is worth 12%. What is the present value of stream?
10. An investor is 50 years of age today. He will retire at the age of 60. In order to receive Rs. 2,00,000 annually for 10 years after retirement, how much amount should he have at the time of retirement? Assume the required rate of return is 10 per cent. 11. Emerson wishes to purchase an annuity a nnuity that will pay him $ 7000 7 000 a year for the rest of his life. The Philo Life Insurance Company figures that his life expectancy is 20 years, based on actuary tables. The company imputes a compound annual interest rate of 6% in its annuity contracts. 11.1. How much will Emerson have to pay for annuity? 11.2. How much would he have to pay if the interest rate were 8%? 12. Mr. Rohit has borrowed a loan of Rs. 5,00,000 to construct his house which repayable in 12 equal equal annual annual instal instalmen ments ts the first first being being paid paid at the end of first year. year. The rate of interest interest chargeable on this loan is 4% p.a. compounded. How much equal annual instalments payable to amortize said loan?
