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Christy Reed made a \(2,000 deposit in her savings account on her 21st birthday, and she has made another \)2,000 deposit on every birthday since then. Her account earns 7 percent compounded annually. How much will she have in the account after she makes the deposit on her 32nd birthday?

Short Answer

Expert verified

The future value on her 32nd birthday will be $35,776.90.

Step by step solution

01

Identification of the required information

Payment (PMT) = $2,000

Period (n) = 12, (From 21 to 32)

Interest Rate (i) = 7%

02

Future value (FV)

FV=PMT×1+in-1i=$2,000×1+7%12-17%=$35,776.90

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Most popular questions from this chapter

Question:Beasley Ball Bearings paid a \(4 dividend last year. The dividend is expected to grow at a constant rate of 2 percent over the next four years. The required rate of return is 15 percent (this will also serve as the discount rate in this problem). Round all values to three places to the right of the decimal point where appropriate.

a. Compute the anticipated value of the dividends for the next four years. That is, compute D1, D2, D3, and D4; for example, D1 is \)4.08 (\(4 3 1.02).

b. Discount each of these dividends back to present at a discount rate of 15 percent and then sum them.

c. Compute the price of the stock at the end of the fourth year (P4). P4 5 D5 ______ Ke 2 g (D5 is equal to D4 times 1.02.)

d. After you have computed P4, discount it back to the present at a discount rate of 15 percent for four years.

e. Add together the answers in part b and part d to get P0, the current value of the stock. This answer represents the present value of the four periods ofdividends, plus the present value of the price of the stock after four periods (which in turn represents the value of all future dividends).

f. Use Formula 10-8 to show that it will provide approximately the same answer as part e. P0 5 D1 ______ Ke 2 g For Formula 10-8, use D1 5 \)4.08, Ke 5 15 percent, and g 5 2 percent. (The slight difference between the answers to part e and part f is due to rounding.)

g. If current EPS were equal to $4.98 and the P/E ratio is 1.2 times higher than the industry average of 6, what would the stock price be?

h. By what dollar amount is the stock price in part g different from the stock price in part f?

i. In regard to the stock price in part f, indicate which direction it would move if (1) D1 increases, (2) Ke increases, and (3) g increases

Larry Davis borrows $80,000 at 14 percent interest toward the purchase of a home. His mortgage is for 25 years.

a.How much will his annual payments be? (Although home payments are usually on a monthly basis, we shall do our analysis on an annual basis for ease of computation. We will get a reasonably accurate answer.)

b.How much interest will he pay over the life of the loan?

c.How much should he be willing to pay to get out of a 14 percent mortgage and into a 10 percent mortgage with 25 years remaining on the mortgage?

Assume current interest rates are 10 percent. Carefully consider the timeb value of money. Disregard taxes.

You invest a single amount of $10,000 for 5 years at 10 percent. At the end of 5 years you take the proceeds and invest them for 12 years at 15 percent. How much will you have after 17 years?

What is the present value of a. $7,900 in 10 years at 11 percent?

You will receive \(6,800 three years from now. The discount rate is 10 percent. a. What is the value of your investment two years from now? Multiply \)6,800 3 (1/1.10) or divide by 1.10 (one year’s discount rate at 10 percent).

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