# Present Value Analysis

**PV Set #1 — FROM CHAPTER 9 –> 2,3,5,6,7,8,9,13 (just calc monthly payment), 14,16,17,18b,19,20,22,23,25a**

2. Find the FV of $10,000 invested now after five years if the annual interest rate is 8 percent.

a. What would be the FV if the interest rate is a simple interest rate?

b. What would be the FV if the interest rate is a compound interest rate?

3. Determine the future values (FVs) if $5,000 is invested in each of the following situations:

a. 5 percent for ten years

b. 7 percent for seven years

c. 9 percent for four years

5. Find the present value (PV) of $7,000 to be received one year from now assuming a 3 percent annual discount interest rate. Also calculate the PV if the $7,000 is received after two years.

6. Determine the present values (PVs) if $5,000 is received in the future (i.e., at the end of each indicated time period) in each of the following situations:

a. 5 percent for ten years

b. 7 percent for seven years

c. 9 percent for four years

7. Determine the present value (PV) if $15,000 is to be received at the end of eight years and the discount rate is 9 percent. How would your answer change if you had to wait six years to receive the $15,000?

8. Determine the future value (FV) at the end of two years of an investment of $3,000 made now and an additional $3,000 made one year from now if the compound annual interest rate is 4 percent.

9. Assume you are planning to invest $5,000 each year for six years and will earn 10 percent per year. Determine the future value (FV) of this annuity if your first $5,000 is invested at the end of the first year.

13. Determine the annual payment on a $15,000 loan that is to be amortized over a four-year period and carries a 10 percent interest rate. Prepare a loan amortization schedule for this loan.

14. You are considering borrowing $150,000 to purchase a new home.

a. Calculate the monthly payment needed to amortize an 8 percent fixed-rate 30-year mortgage loan.

b. Calculate the monthly amortization payment if the loan in (a) was for 15 years.

16. Use a financial calculator or computer software program to answer the following questions:

a. What would be the future value (FV) of $15,555 invested now if it earns interest at 14.5 percent for seven years?

b. What would be the FV of $19,378 invested now if the money remains deposited for eight years and the annual interest rate is 18 percent?

17. Use a financial calculator or computer software program to answer the following questions:

a. What is the present value (PV) of $359,000 that is to be received at the end of twenty-three years if the discount rate is 11 percent?

b. How would your answer change in (a) if the $359,000 is to be received at the end of twenty years?

18. Use a financial calculator or computer software program to answer the following questions:

b. What would be the present value (PV) of a $9,532 annuity for which the first payment will be made beginning one year from now, payments will last for twenty-seven years, and the annual interest rate is 13 percent?

19. Use a financial calculator or computer software program to answer the following questions.

a. What would be the future value (FV) of $19,378 invested now if the money remains deposited for eight years, the annual interest rate is 18 percent, and interest on the investment is compounded semiannually?

b. How would your answer for (a) change if quarterly compounding were used?

20. Use a financial calculator or computer software program to answer the following questions.

a. What is the present value (PV) of $359,000 that is to be received at the end of twenty-three years, the discount rate is 11 percent, and semiannual discounting occurs?

b. How would your answer for (a) change if monthly discounting were used?

22. Answer the following questions.

a. What is the annual percentage rate (APR) on a loan that charges interest of .75 percent per month?

b. What is the effective annual rate (EAR) on the loan described in (a)?

23. You have recently seen a credit card advertisement stating that the annual percentage rate (APR) is 12 percent. If the credit card requires monthly payments, what is the effective annual rate (EAR) of interest on the loan?

1. You annually invest $1,500 in an individual retirement account (IRA) starting at the age of 20 and make contributions for 10 years. Your twin sister does the same starting at age 30 and makes contributions for 30 years. Both of you earn 7% annually on you investment. Who has the larger amount at age 60?

2. If a parent wants to have $100,000 to send a newborn child to college, how much must be invested annually for 18 years if the funds earn 9%?

3. An investment generates $10,000 per year for 25 years. If you can earn 10% on other investments, what is the current value of this investment? If its current price is 120,000, should you buy it?

4. You are offered an annuity that will pay $10,000 a year for 10 years (that is 10 payments) starting after five years have elapsed. If you seek an annual return of 8%, what is the maximum amount you should pay for this annuity?

5. You want your salary to double in six years. At what annual rate of growth must you salary increase to achieve your goals.

6. Each year you invest $2,000 in an account that earns 5% annually. How long will it take for you to accumulate $50,000?

7. Auntie Kitty sells her house for $200,000, which is then invested to earn 6% annually. If her life expectancy is 10 years, what is the maximum amount she can annually spend on a nursing home, doctors, and taxes?

8. You win a judgment in an auto accident for $100,000. You immediately receive $25,000 but must pay your lawyer’s fee of $15,000. In addition, you will receive $2,500 a year for 20 years for a total of $50,000 after which the balance owed ($25,000) will be paid. If the interest rate is 7%, what is the current value of your settlement?

9. Uncle Fred recently died and left $325,000 to his 50-year-old favorite niece. She immediately s[en $100,000 on a town home but decided to invest the balance for her retirement at age 65. What rate of return must she earn on her investment over the next 15 years to permit her to withdraw $750,000 at the end of each year through age 80 if her funds earn 10% annually during retirement?

10. A $1,000,000 state lottery prize is spread evenly over 10 years ($100,000 a year), or you may take a lump distribution of $654,000. If you can earn 7%, which alternative is better?

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