 # What Is The Future Value Formula For Annuities?

When you purchase an annuity, you are buying an insurance product that will provide you with regular retirement income in the future. Your annuity will earn interest over time, so the future value of this annuity may be more than what you pay into the annuity at the start. Whether you make your annuity purchase via regular payments over a period of several years or with one lump sum payment, it's helpful to calculate the future value formula for the money to understand exactly how much your annuity will eventually be worth.

Here's how the future value formula works and how you can use it to make the best decisions for your annuity.

## The Time Value of Money

The time value of money is the idea that a specific amount of money in the future does not have the same value as the exact same amount of money currently. That's because you can invest that money now for a bigger payoff later.

For example, let's say two different investors put \$50,000 into an investment with a guaranteed 6% interest rate. The first one invests a \$50,000 lump sum today, while the second invests \$50,000 in \$5,000 installments over a period of ten years. The first investor gets to take advantage of the growth of the full \$50,000 over those ten years, while the second investor's money will grow more slowly.

Here's how each of these calculations works.

### Future Value Formula for a Lump Sum Annuity

The formula used to calculate the future value of an annuity depends first on whether you have made a lump sum investment or are paying in installments. The calculation for a lump sum annuity investment is:

Future Value for a Lump Sum Annuity = PV x (1 + r)n

To make this calculation, you'll need to know the following factors:

• PV = The present value (or the amount you are investing)
• r = The interest rate (also known as the discount rate)
• n = The number of years in the future you want to predict

For example, say an investor purchases an annuity with a guaranteed 6% interest rate with a \$50,000 lump sum. The future value after ten years will look like this:

Future Value = \$50,000 x (1 + .06)10

= \$50,000 x (1.06)10

= \$50,000 x (1.7908476)

= \$89,542.38

The future value of this annuity will be \$89,542.38 in ten years. If your algebra skills are a little rusty, an online calculator can help.

### Future Value Formula for an Ordinary Annuity

Ordinary annuities pay interest at the end of each period. This is the most common type of annuity, and the following formula is the one most people will use if they are buying an annuity in installments.

Future Value for an Ordinary Annuity = PMT x ((1 + r)n − 1) / r

In this calculation, you'll use these factors:

• PMT = The dollar amount of each payment
• r = The interest rate
• n = The number of years you will be making payments

For a \$50,000 annuity with a guaranteed 6% interest rate purchased in \$5,000 installments over ten years, the future value formula would look like this:

Future Value = \$5,000 x ((1 + .06)10 − 1) / .06

= \$5,000 x ((1.06)10 − 1) / .06

= \$5,000 x (1.7908476 − 1) / .06

= \$5,000 x 0.7908476 / .06

= \$5,000 x 13.180795

= \$65,903.97

The future value of this ordinary annuity is \$65,903.97.

### Future Value Formula for an Annuity Due

An annuity due pays interest at the beginning of each period. Since the annuity due pays interest earlier, there is more time for that interest to compound, which is why the formula for calculating the future value is slightly different. Here's how this one works:

Future Value for an Annuity Due = PMT x (((1 + r)n − 1) / r) x (1 + r)

Using the same values as the previous example, here's how you would calculate the future value of an annuity due:

Future Value = \$5,000 x (((1 + .06)10 − 1) / .06) x (1 + .06)

= \$5,000 x (((1.06)10 − 1) / .06) x (1 + .06)

= \$5,000 x ((1.7908476 − 1) / .06) x (1 + .06)

= \$5,000 x (0.7908476 / .06) x (1 + .06)

= \$5,000 x 13.180795 x (1.06)

= \$5,000 x 13.971643

= \$69,858.22

For an annuity due, even though you're making the same payments as in the ordinary annuity, the outcome is different because of when the interest is paid. You can use an online calculator to more easily calculate both an ordinary annuity and an annuity due and compare their differences.

## Planning Your Retirement with Annuities

In addition to making these calculations yourself, you may also decide to run your plans by a financial advisor to make sure you've thought through all the potential outcomes. Understanding the future value of your annuity can help you make the best financial decisions for your retirement. 