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Number of Periods and Percent Annual Interests

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1. Calculating the Number of Periods - You're trying to save to buy a new $170,000 Ferrari. You have $40,000 today that can be invested at your bank. The bank pays 5.3 percent annual interest on its accounts.

(a) How long will it be before you have enough to buy the car?

(b) If you believe your mutual fund can achieve a 12 percent annual rate of return and you want to buy the car in 9 years on the day you turn 30, how much must you invest today?

2. Calculating Future Values - You have just made your first $4,000 contribution to your retirement account. Assuming you earn an 11 percent rate of return and make no additional contributions, what will your
account be worth when you retire in 45 years? What if you wait 10 years before contributing? (Does this suggest an investment strategy?

3. Calculating Interest Rates - Assume the total cost of a college education will be $290,000 when your child enters college in 18 years. You presently have $55,000 to invest. What annual rate of interest must you earn on your investment to cover the cost of your child's college education?

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This solution is comprised of a detailed explanation to answer how long will it be before you have enough to buy the car.

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1. Calculating the Number of Periods - You're trying to save to buy a new $170,000 Ferrari. You have $40,000 today that can be invested at your bank. The bank pays 5.3 percent annual interest on its accounts.

(a) How long will it be before you have enough to buy the car?

FV = PV (1+i)n where PV is the present value
FV is the future value
i is the interest rate
n is the period

$170,000 = $40,000(1 + 0.053)n
4.25 = (1.053)n
ln 4.25 = n ln ...

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