Session 5 Homework

Time Value of Money - Answer the following questions:

1. Assume that 1 year from now; you will deposit $1,000 into a savings account that

pays 8%.

a. If the Bank compounds interest annually, how much will you have in your account 4 years from now?

b. What would your balance 4 year from now be if the bank used quarterly compounding rather than annual compounding?

c. Suppose you deposited the $1,000 in 4 payments of $250 each at Years 1, 2, 3, and 4. How much would you have in your account at Year 4, based on 8% annual compounding?

2. Assume that 4 years from now you will need $1,000. Your bank compounds interest at an 8% annual rate.

a. How much must you deposit 1 year from now to have a balance of $1,000 4 years from now?

b. If you want to make equal payments at Years 1 through 4 to accumulate the $1,000, how much each of the 4 payments be?

c. If your father were to offer either to make the payments calculated in part b or to give you a lump sum of $750 1 year from now, which would you choose?

d. If you have only $750 1 year from now, what interest rate, compounded annually, would you have to earn to have the necessary $1,000 4 years from now?

e. Suppose you can deposit only $186.29 each at Years 1 through 4, but you still need $1,000 at Year 4. What interest rate, with annual compounding, must you seek out to achieve your goal?

3. Find the amount to which $500 will grow under each of the following conditions:

a. 12% compounded annually for 5 years

b. 12% compounded semiannually for 5 years

c. 12% compounded quarterly for 5 years

d. 12% compounded monthly for 5 years

4. While Mary was a student at the University, she borrowed $12,000 in student loans at an annual interest rate of 9%. If Mary repays $1,500 per year, how long, to the nearest year, will it take her to repay the loan?

5. You win a lottery that pays you $100 a year for ever and agrees to pay all of your ancestors $100 forever. What is the present value of your winnings?