What Is the Present Value of an Annuity?

The present value of an annuity is the amount of money you would need today to make a series of regular payments in the future, considering that money earns interest over time. It’s like asking: How much is a set of future payments worth right now?

When payments are made regularly, and interest is applied, each payment is worth less in today's money because of the time value of money. Money now is worth more than money later because you can invest it and earn interest.

Example

Imagine you will make 4 payments of $100 each, every 3 months (quarterly) for a year. The annual interest rate is 10%, compounded quarterly. This means that the interest per quarter is:

We need to calculate how much these payments are worth today.

1 - Find the present values of each payment

1. Payment 1 (3 months from now):
   Since this payment is 1 quarter away, it will experience one period of interest before payment. To find its present value
   

1. Payment 2 (6 months from now):
   This payment is 2 quarters away, so it will experience 2 periods of interest:

1. Payment 3 (9 months from now):
   This payment is 3 quarters away, so it will experience 3 periods of interest:

1. Payment 4 (12 months from now):
   This payment is 4 quarters away, so it will experience 4 periods of interest:

2 - Add Up All Present Values

Now, add up the present values of all 4 payments to find the total present value of the annuity

substitute the values

and simplify

Final Answer

The present value of the annuity with $100 quarterly payments over 1 year at 10% annual interest (compounded quarterly) is approximately $376.20.