A deferred annuity is a series of regular payments that begin after a delay (or deferment period). To calculate its present value, you first discount the annuity payments back to the time when they begin and then discount that amount further to today’s value.

Steps to Calculate the Present Value of a Deferred Annuity

1. Find the present value of the annuity as if it starts at the end of the deferment period.
2. Discount the present value back to today using the interest rate.

The present value of an ordinary annuity (starting immediately) is given by:

To account for the deferment period, discount this result back to today using:

Where:

• $P_{\text{annuity}}$ = present value of the annuity at the time payments start
• $R$ = regular payment amount
• $i$ = interest rate per payment period
• $n$ = number of payments in the annuity
• $t$ = number of periods in the deferment (delay) period

Example

You will receive $500 annually for 4 years, but the payments start 3 years from now. The interest rate is 6% annually. What is the present value today?

Step 1: Find the Present Value of the Annuity at the Start of Year 3

We first calculate the present value of the annuity payments as if they begin at the end of year 3 using the formula

Substitute the values:

• $R=500$,
• $i=0.06$ (annual interest rate),
• $n=4$ (4 payments).

At the start of year 3, the present value of the annuity is 1,732.55.

Step 2: Discount the Present Value Back to Today

Now, discount the value of $1,732.55$ back 3 years to find the present value today

Substitute the values:

• $P_{\text{annuity}}=1,732.55$,
• $i=0.06$,
• $t=3$ (3-year deferment period).

Final Answer:

The present value of the deferred annuity is approximately $1,454.68.

Explanation

Receiving $500 dollars annually for 4 years beginning 3 years is equivalent to:
Investing $1,454.68 today in an account with a 6% annual interest rate, and withdrawing $500 each year after 3 years.

This allows you to adequately evaluate the value of the deferred annuity using the value of todays money.