Assignment No. 1 Chapter No. 03 The Time Value of Money Managerial Finance (M.com-2) The following are exercises in future (terminal) values: a. At the end of three years, how much is an initial deposit of $100 worth, assuming a compound annual interest rate of (i) 100 percent? (ii) 10 percent? (iii) 0 percent? b. At the end of five years, how much is an initial $500 deposit followed by five yearend, annual $100 payments worth, assuming a compound annual interest rate of (i) 10 percent? (ii) 5 percent? (iii) 0 percent? c. At the end of six years, how much is an initial $500 deposit followed by five year-end, annual $100 payments worth, assuming a compound annual interest rate of (i) 10 percent? (ii) 5 percent? (iii) 0 percent? d. At the end of three years, how much is an initial $100 deposit worth, assuming a quarterly compounded annual interest rate of (i) 100 percent? (ii) 10 percent? e. Why do your answers to Part (d) differ from those to Part (a)? f. At the end of 10 years, how much is a $100 initial deposit worth, assuming an annual interest rate of 10 percent compounded (i) annually? (ii) semiannually? (iii) quarterly? (iv) continuously? The following are exercises in present values: a. $100 at the end of three years is worth how much today, assuming a discount rate of (i) 100 percent? (ii) 10 percent? (iii) 0 percent? b. What is the aggregate present value of $500 received at the end of each of the next three years, assuming a discount rate of (i) 4 percent? (ii) 25 percent? c. $100 is received at the end of one year, $500 at the end of two years, and $1,000 at the end of three years. What is the aggregate present value of these receipts, assuming a discount rate of (i) 4 percent? (ii) 25 percent? d. $1,000 is to be received at the end of one year, $500 at the end of two years, and $100 at the end of three years. What is the aggregate present value of these receipts assuming a discount rate of (i) 4 percent? (ii) 25 percent? e. Compare your solutions in Part (c) with those in Part (d) and explain the reason for the differences. 3. Joe Hernandez has inherited $25,000 and wishes to purchase an annuity that will provide him with a steady income over the next 12 years. He has heard that the local savings and loan association is currently paying 6 percent compound interest on an annual basis. If he were to deposit his funds, what year-end equal-dollar amount (to the nearest dollar) would he be able to withdraw annually such that he would have a zero balance after his last withdrawal 12 years from now? 4. You need to have $50,000 at the end of 10 years. To accumulate this sum, you have decided to save a certain amount at the end of each of the next 10 years and deposit it in the bank. The bank pays 8 percent interest compounded annually for long-term deposits. How much will you have to save each year (to the nearest dollar)? 10. Suppose you were to receive $1,000 at the end of 10 years. If your opportunity rate is 10 percent, what is the present value of this amount if interest is compounded (a) annually? (b) quarterly? (c) continuously? Suppose that an investment promises to pay a nominal 9.6 percent annual rate of interest. What is the effective annual interest rate on this investment assuming that interest is compounded (a) annually? (b) semiannually? (c) quarterly? (d) monthly? (e) daily (365 days)? (f ) continuously? (Note: Report your answers accurate to four decimal places – e.g., 0.0987 or 9.87%.)