How to Calculate the Present Value of a Growing Annuity Using the Future Value

By: Ryan Cockerham | Reviewed by: Ashley Donohoe, MBA | Updated May 16, 2019

When you initiate an annuity plan for your retirement, you are likely organizing a financial platform yourself that you won't actually be using for years. After all, the strength and appeal of an annuity lies in the fact that individuals can make recurring payments into what is essentially a retirement account and then withdraw these funds in combination with accrued interest once they reach the age of 59.5. If you have begun contributing to an annuity, you may be curious how you can calculate both the present and future value of the fund based on the data you currently have on hand. Fortunately, this process can be accomplished relatively easily using a few simple mathematical formulas.

Tip

You can calculate the present value of your fixed annuity using the future value determined by the insurer and a variety of other data points. Fortunately, the formula that accompanies these calculations is relatively straightforward.

Basics of Annuities

When you start an annuity with an insurance company, you will likely be required to choose from one of three primary varieties available, those being a variable annuity, an indexed annuity and a fixed annuity. Each of these annuity formats differs with regard to the types of returns the annuity holder can expect, as well as the level risk associated with the holding.

How Fixed Annuities Work

With a fixed annuity, individuals are guaranteed payout based on the size and frequency of their contributions. It is these annuities that allow for the highest degree of predictability and calculation with respect to determining present values based on future values.

Fixed annuities are defined by a number of key features, perhaps one of the most important being a guaranteed minimum interest rate. When an individual initiates a fixed rate annuity, they are protected by what is commonly referred to as an initial guarantee period. During this time, the interest rate attached to the annuity will not deviate from what has been agreed to between the annuity holder and the insurance company.

However, following the end of the initial guarantee period, the insurance company will adjust the interest rate on a regular basis based on a variety of parameters, one of the most significant being the current yield being produced by the insurance company's own investment. Although market volatility will always act as a hugely influential force on investment yield, a fixed annuity guarantees that the insurer cannot lower rates beyond the guarantee which has been provided to the annuity holder.

Calculating Annuity Values Using Current Formulas

In order to calculate the present value of an annuity based on the pre-determined future value, you can use the following formula:

Pv = Fv / (1 + r)^n

In this formula, Pv represents the present value of the annuity, Fv represents the future value of the annuity, "r" stands for the interest rate attached to the annuity and "n" represents the number of cash flows remaining. With this information on hand, you should be able to quickly begin to determine the present value of your fund.

Example Scenario and Calculation

As an example, consider the following scenario. With a fixed rate annuity, you know that, based on your current payments, the sum total at the time of withdrawal will be $500,000. Therefore, Pv = $500,000. If your annuity is currently growing at a rate of 2.5 percent annually, the decimal-formatted variation of this number will be substituted for "r."

If you have two years of contributions remaining, you will use this number for "n." Keep in mind, however, that you will need to convert the interest rate in your formula to a monthly rate of accrual if you have less than a year's worth of payments remaining.

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About the Author

Ryan Cockerham is a nationally recognized author specializing in all things business and finance. His work has served the business, nonprofit and political community. Ryan's work has been featured on PocketSense, Zacks Investment Research, SFGate Home Guides, Bloomberg, HuffPost and more.

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