1. Future value of a single sum

A sum of $1,000 is deposited at 8% interest, compounded annually for 5 years. What is the future value?

2. Future value of a single sum – more frequent compounding

$1,000 is invested for 5 years in an account earning 8% annual interest, compounded semiannually. What will be the future value in 5 years?

3. Present value of a single sum

An individual will receive $1,000 in 5 years. How much is this worth today if the interest rate (opportunity cost) on investments is 8%, compounded annually?

4. Present value of a single sum – more frequent compounding

An individual will receive $1,000 in 5 years. How much is this worth today if the interest rate is 8%, compounded semiannually?

5. Number of compounding periods

An individual has $1,000 to invest. He wants to accumulate $3,670 and can earn 8% annual interest on investments, compounded annually. How many years will it take to attain his goal?

6. Number of compounding periods – more frequent compounding

An individual has $1,000 to invest. She wants to accumulate $3,670 and can earn 8% interest, compounded semiannually. She wants to accumulate $3,670. How many years will it take to attain her goal?

7. Interest rate

An individual has $1,000 to invest and wants to accumulate $1,470 in 5 years. What interest rate, compounded annually, must be earned to accomplish the objective?

8. Interest rate – more frequent compounding

An individual has $1,000 to invest and wants to accumulate $1,470 in 5 years. What interest rate, compounded semiannually, must be earned to accomplish the objective?

9. Present value of an annuity

An individual expects to receive a payment of $1,000 at the end of the next 5 years. If the expected interest rate is 8%, compounded annually, what is the annuity worth today?

10. Future value of an annuity

An individual invests $1,000 at the beginning of each of the next 5 years. The interest rate is 8%, compounded annually. What will be the value of the investment in 5 years?

11. Future value of an annuity – more frequent compounding

An individual invests $1,000 at the beginning of each of the next 5 years. The interest rate is 8%, compounded semiannually. What will be the value of the investment in 5 years?

12. Annuities – more frequent investments and compounding

An individual invests $500 at the beginning of each 6-month period over the next 5 years. The interest rate is 8%, compounded semiannually. What will be the value of the investment in 5 years?

13. Periodic payment or receipt

An individual wants to purchase an automobile for $10,000 and can finance the purchase at 8% interest, compounded annually, for 4 years. What payment will be required at the end of each of the 4 years?

14. Periodic payment or receipt – more frequent compounding

Same facts as in #13 except the interest is compounded monthly. What will be the monthly payment?

The last two problems involve calculating rate of return and present value for unequal cash flows.

15. Calculating internal rate of return

An individual purchases a plot of land for $16,000. A year after the land is purchased, he makes improvements costing $4,000; the next year, he makes improvements costing $3,000. At the end of the third year, the land is rented to a tenant who pays $3,000 for the entire year, and $3,500 at the end of the fourth year. At the end of the fifth year, the land is sold for $28,600. What has been the rate of return on this investment?

16. Calculating present value

An individual is considering investing in a building. She would like an average return of 12%, compounded annually, on the investment. She expects to keep the building for 3 years, then sell it for $290,000. She anticipates expenses at the end of the first year of $23,000, $11,000 at the end of the second year, and $5,000 at the end of the third year. In addition, she expects rental revenues of $9,000 and $11,000 at the end of the first and second years, respectively. What price should she pay for the building to achieve he required 12% return?