Questions for Practice: Time Value of Money

Q1) Mr. Rohit is considering two options for investing Rs. 5,000 for 4 years. In the first option, he will get an assured return of Rs. 7,000 plus percentage gain on the sensex at the end of 4th year over today’s closing index. The second option assures him an interest rate of 15% p.a. compounded annually. Today’s closing index =4000, Sensex at the end of 4th year =5000. What amount will Rohit receive at the end of 4th year, if he is considering, the two options independently?

Q2) What is the future value of Rs.20, 000 invested now for a period of 5 years at an interest rate of 8%?

Q3) What is the future value of the following series of payments @ 5% rate of interest at the end of 5 years?

1st year = Rs.2, 0002nd year = Rs.3, 0003rd year = Rs.4, 0004th year = Rs.5, 0005th year = Rs.6, 000

Q4) An investment company offers to pay Rs.25, 959 at the end of 10 years to investors who deposit annually Rs.1, 000. The implied interest rate is_________________

Q5) In order to buy a car, on January 1, 2009, presently available at a price of Rs.2, 50,000, you started to deposit your money in a monthly recurring deposit scheme of a bank from December 31, 2005. The bank offers a rate of interest of 12 % p.a. compounded monthly. If the car price is expected to go up by 4 % p.a., how much amount should you deposit every month in that scheme? (Round off your answer to the nearest integer)

Q6) X deposited Rs.1, 00,000 on retirement in a bank which can be withdrawn Rs.16, 274 annually for a period for 10 years. What is the interest rate?

Q7) Vision Ltd., an NBFC offers car loans with two schemes. Scheme A offers 10% discount on cash payment. Scheme B asks for a down payment of Rs. 18,000 and Rs.4, 100 per month for 5 years. If the cost of the car is Rs.2.5 lakhs and the required rate of return is 9%, Find the cash outflow in both schemes.

Q8) How much amount should be deposited today in order to receive Rs.5, 000 next year, and which grows at the rate of 4% forever? Assume that the discount rate is 14% per annum.

Q9) Ms. Kusum has retired recently. She received Rs.5 lakh as her retirement benefits, which she had invested in a bank at 15% rate of interest. If she expects to live

independently for another 15 years, how much money she can withdraw at the end of every year so as to leave a nil balance in her account at the end of maturity?

Q10) Mr. Prasad is considering to purchase a commercial complex that will generate a net cash flow of Rs.4, 00,000 at the end of one year. The future cash flows are expected to grow at the rate of 4% per annum. Mr. Prasad’s required rate of return is 12%. Mr Prasad would be willing to pay the amount of ________________ for the complex if he wishes to sell it at the end of four years at Rs.40lakh, net of transaction costs.

Q11) The present value of cash flows of Rs.950 per year forever at an interest rate of 8% and 10% are_____________ and ___________________ respectively.

Q12) The present value of Rs.4, 500 receivable in 7 years at a discount rate of 15% is__________

Q13) The present value of an annuity of Rs.8, 000 starting in 7 years time lasting for 7 years at a discount rate of 10% is_________________

Q14) The present value of an annuity of Rs.550 starting after 1 year for 6 years at an interest rate of 12% is ________________

Q15) The present value of an annuity of Rs.1, 300 starting immediately and lasting until 9th year at a discount rate of 20% is_______________

Q16) The present value of perpetuity of Rs.800 starting in the beginning of year 3 at a discount rate of 18% is_______________

Q17) ________________ is the present worth of operating expenditures of Rs. 4,00,000 per year which are assumed to be incurred continuously throughout in 8 year period if the effective annual rate of interest is 12%.

Q18) Kiran Automobiles purchases machinery for Rs.8, 00,000 by making a down payment of Rs.1, 50,000 and remainder in equal installments of Rs.1, 50,000 for six years. The rate of interest to the firm is_______________

Q19) Ten years from now Mr. will start receiving a pension of Rs8, 000 a year. The payment will continue for sixteen years. If his interest rate is 10%, now the worth of pension is_____________

Q20) Assume that a deposit is to be made at year zero into an account that will earn 8% compounded annually. It is desired to withdraw Rs.6, 000 after three years from now and Rs.7, 000 after six years from now. The size of the year zero deposit that will produce these future payments is _______________