# Number of Periods and Percent Annual Interests

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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#### Solution Preview

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 ...

#### Solution Summary

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

Time Value of Money and Capital Budgeting

Problem: If you invest $8000 per period for the following number of periods, how much would you have?

a.7 years at 9 percent

b.40 years at 11 percent

Problem: The western sweeptakes has just informed you that you have won $1 million. The amount is to be paid at the rate of $50000 a year for the next 20 years. With a discount rate of 12%, what is the present value of your winnings.

Problem: Dr Oats, a nutrition professor, invests $8000 in a piece of land that is expected to increase in value by 14% per year for the next five years. She will then take the proceeds and provide herself with a 10-year annuity. Assuming a 14 percent interest rate for the annuity, how much will this annuity be?

Problem: Essex Biochemical Company has a $1000 par value bond that pays 10 percent annual interest. The company yield to maturity on such bonds in the market is 7 percent. Compute the price of the bonds for these maturity dates:

a.30 years

b.15 years

c.1 year

Problem: Bonds issued by Coleman Manufacturing Company have a par value of $1,000, which, of course, is also the amount of principal to be paid at maturity. The bonds are currently selling for $850. They have 10 years remaining to maturity. The annual interest payment is 8 percent ($80). Compute the approximate yield to maturity.

Problem: Laser optics will pay a common stock dividend of $1.60 at the end of year (D1). The required rate of return on common stock (Ke) is 13%. The firm has a constant growth rate(g) of 7 percent. Compute the current price of the stock(Po).

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