# Present Value (PV) of an Annuity Calculator

LAST UPDATE: September 27th, 2019

### What is the Present Value (PV) of an annuity?

The present value (PV) of an annuity is the value today of a series of payments in the future. It uses a payment amount, number of payments, and rate of return to calculate the value of the payments in today’s dollars.

### PV of an annuity formula – how the Present Value of an Annuity is calculated

$\text{Present Value} = (\frac{\text{Payment}}{\text{Rate or Return}}) \times (1 - \frac{1}{(1 + \text{Rate of Return})^\text{Number of Periods}})$

Where:

• Payment” is the payment each period.
• Rate of Return” is a decimal rate of return per period (the calculator above uses a percentage). A return of 2.2% per period would be calculated in the formula as “0.022”.
• Number of Periods” is the number of periods (any payments).

### Example

We will receive \$100 each year for the next 10 years. The interest rate at the moment is 2.2% compounded annually. What is the present value of this annuity?
$\text{Present Value} = (\frac{100}{0.022}) \times (1 - \frac{1}{(1 + 0.022)^{10}})$
$\text{Present Value} = 4,545.45454545 \times (1 - \frac{1}{(1.022)^{10}})$
$\text{Present Value} = 4,545.45454545 \times (1 - \frac{1}{1.243108})$
$\text{Present Value} = 4,545.45454545 \times (1 - 0.80444)$
$\text{Present Value} = 4,545.45454545 \times 0.19556$
$\text{Present Value} = 888.91$

### What is the difference between an annuity and an annuity due?

The two are very similar. With an annuity, the payment occurs at the end of the period. With an annuity due, the payment occurs at the beginning of the period.

### What is the difference between an annuity and a perpetuity?

An annuity stops after a specific amount of time, a perpetuity goes on forever (in theory).

### What is the difference between the present value and future value of an annuity?

The present value of an annuity is the value of the annuity in today’s dollars. The future value of the annuity is the value of the annuity on the date it is finished.