The correct answer is A. future value of perpetuity.
A perpetuity is a series of equal payments that are made forever. The future value of a perpetuity is the total amount of money that will be paid out over the course of the perpetuity, assuming that the payments are made at regular intervals and that the interest rate remains constant.
The formula for the future value of a perpetuity is:
$FV = P\frac{r}{1-r}$
where:
- $FV$ is the future value of the perpetuity
- $P$ is the present value of the perpetuity
- $r$ is the interest rate
The present value of a perpetuity is the amount of money that would need to be invested today in order to generate the same series of payments as the perpetuity. The formula for the present value of a perpetuity is:
$PV = \frac{FV}{r}$
A due perpetuity is a perpetuity in which the payments are made at the beginning of each period. A deferred perpetuity is a perpetuity in which the first payment is made after a certain number of periods.
In the case of a perpetuity, the payment is divided by the interest rate to get the present value of the perpetuity. This is because the present value of a perpetuity is the amount of money that would need to be invested today in order to generate the same series of payments as the perpetuity. The interest rate is used to discount the future payments back to their present value.