# time value of money questions, business and finance homework help

1. You are schedule to receive \$10,000 in two years. When you receive it, you will immediately invest it for six more years in a savings account that earns 5% annually. How much money will you have in eight years?

2. Investment X offers to pay you \$3,700 every year for the next nine years, whereas investment Y offers to pay you \$5,500 per year for the next five years. If the interest rate is 6%, which investment has the higher present value?

3. You want to deposit \$X in your retirement account today. You plan to retire in 35 years and make your first withdrawal from your account (at time 35) of \$100,000; you will make 19 additional annual withdrawals (your last one is at time 54) but each one is 2% larger that the previous one to compensate for inflation. How much is X if your retirement account earns a 5.3% interest rate?

4. You are thinking of building a new machine that will save your company \$1,000 in the first year. The machine will then begin to wear out so that the savings decline at a rate of 2% per year forever. What is the present value of the savings if the interest rate is 5% per year? (Hint: this is a growing perpetuity.) 1

5. Your parents wanted to have \$160,000 saved for college by your 18th birthday and they started saving on your first birthday. They saved the same amount each year on your birthday and earned 8% per year on their investments. How much would they have to save each year to reach their goal? (Hint: \$160,000 is a future value, find first its PV and then solve for the amount.)

6. Suppose the Texas lottery advertises that it pays its winner \$10 million. However, this prize money is paid at the rate of \$500,000 each year (with the first payment being immediate) for a total of 20 payments. What is the present value of this prize at 10% annual interest rate?

7. In the year 2000, the New York Mets (a professional baseball team) owed Bobby Bonilla (a baseball player) \$5.9 million. Instead of paying the amount on the spot, the Mets and Bonilla agreed to defer his compensation in the following way: starting in 2011, Bonilla would receive \$1.2 million every year until 2035 (that is 25 annual payments). Assume the interest rate is 5%, was this a good or bad deal for Bonilla?