# Calculating PV and FV of annuties

1.The present value of an ordinary annuity of $2,350 each year for eight years, assuming an opportunity cost of 11 percent, is

1. $27,869.

2. $ 1,020.

3. $12,093.

4. $18,800.

2.Dan plans to fund his individual retirement account (IRA) with the maximum contribution of $2,000 at the end of each year for the next 10 years. If Dan can earn 10 percent on his contributions, how much will he have at the end of the tenth year?

1. $51,880

2. $20,000

3. $31,874

4. $12,290

3.The present value of a $25,000 perpetuity at a 14 percent discount rate is

1. $178,571.

2. $219,298.

3. $285,000.

4. $350,000.

4.The future value of $200 received today and deposited at 8 percent for three years is

1. $158.

2. $252.

3. $248.

4. $200.

5.The annual rate of return is variously referred to as the

1. opportunity cost.

2. cost of capital.

3. discount rate.

4. all of these.

6.When the amount earned on a deposit has become part of the principal at the end of a specified time period the concept is called

1. discount interest.

2. primary interest.

3. future value.

4. compound interest.

7.In future value or present value problems, unless stated otherwise, cash flows are assumed to be

1. at the beginning of a time period.

2. at the end of a time period.

3. spread out evenly over a time period.

4. in the middle of a time period.

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#### Solution Preview

Solution:

1.The present value of an ordinary annuity of $2,350 each year for eight years, assuming an opportunity cost of 11 percent, is

Present Value of annuity=2350/11%*(1-1/(1+11%)^8=12093.39

Answer is 3. $12,093.

2.Dan plans to fund his individual retirement account (IRA) with the maximum ...

#### Solution Summary

There are 7 basic problems related to time value of money concepts. Solutions depicts the steps to calculate present and future value annuities.

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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