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# Accounting: Future Value, Present Value and Compounded Value

1. How many years in a typical perpetuity?
2. What is the relationship between the future value factor for five years at 5 percent and the present value factor for five years at 5 percent?
3. If a business manager deposits \$30,000 in a savings account at the end of each year for twenty years what will be the value of her investment: at a compound rate of 12 percent? At a compounded rate of 18 percent? What would the outcome be in both cases if the deposits were made at the beginning of each year?
4. The chief financial officer of a home health agency needs to determine the present value of a \$10,000 investment received at the end of year 10. What is the present value if the discount rate is: a. 6 percent b. 9 percent c. 12 percent d. 15 percent?

#### Solution Preview

1. How many years in a typical perpetuity?
By definition, perpetuity is an annuity that has no end, or a stream of cash payments that continues forever. Therefore, there are an unlimited number of years in a perpetuity.

2. What is the relationship between the future value factor for five years at 5 percent and the present value factor for five years at 5 percent?
The future value factor for five years at 5 percent is 1.2763, and it is the inverse of the present value factor for five years at 5 percent, which is 0.78353. In other words, the product of the two factors is 1.

The relationship can be derived as follows:
(1) FV=PV*FV_factor
Move FV_factor to the left:
(2) FV (1/FV_factor) = PV
On the other ...

#### Solution Summary

The future value, present values and compounded values in accounting are examined.

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