## Perpetuity – Present Value

**[Watch video for detailed explanation of concept and formula and also for different types]**

Perpetuity is a sequence of cash flows that continues indefinitely. Perpetuity is an annuity in which the periodic payments or receipts begin on a fixed date and continue indefinitely or perpetually. That is simply an annuity with an extended life.

The formula for calculating the present value of multi period perpetuity is:

Where, R – the payment or receipt each period, i – the interest rate per payment or receipt period.

#### Numerical Problems

**[Watch video for solution of the problems below with explanation]**

Q 1. Calculate the PV of a perpetuity that pays Rs. 100 pa annually in arrears using an annual effective interest rate 10%.

Q 2. Calculate the present value of an annuity that pays Rs. 100 pa quarterly for ever in arrears using an annual effective rate of interest of 10%.