time value of money questions, business and finance homework help

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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.)

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?

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