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?
