How To Calculate The Value Of An Annuity


When planning for retirement, you need to account for the value of any annuities that you own. Trouble is, there’s not just one value of an annuity—there are two: present value and future value.

Understanding the Value of an Annuity

An annuity is a contract between you and an insurance company that’s typically designed to provide retirement income. You buy an annuity either with a single payment or a series of payments, and you receive a lump-sum payout shortly after purchasing the annuity or a series of payouts over time.

An annuity’s value is the sum of money you’ll need to invest in the present to provide income payments down the road.

Using the present value formula helps you determine how much cash you must earmark for an annuity to reach your goal of how much money you’ll receive in retirement.

If your annuity promises you a $50,000 lump sum payment in the future, then the present value would be that $50,000 minus the proposed rate of return on your money.

As you might imagine, the future value of an annuity refers to the value of your investment in the future, perhaps 10 years from today, based on your regular payments and the projected growth rate of your money.

What Is the Present Value of an Annuity?

The present value of an annuity is the total value of all of future annuity payments. A key factor in determining the present value of an annuity is the discount rate. This can be an expected return on investment or a current interest rate.

A lower discount rate results in a higher present value, while a higher discount rate results in a lower present value.

How to Calculate the Present Value of an Annuity

A number of online calculators can compute present value for your annuity. But if you want to figure out present value the old-fashioned way, you can rely on a mathematical formula (with the help of a spreadsheet if you’re comfortable using one). Or you can use an annuity table.

The information you’ll need to calculate present value of an annuity includes:

  • Payment amount. Amount of money you envision getting paid by period (monthly, quarterly or annually).
  • Interest rate. The interest rate per period.
  • Number of time periods. The number of periods applied to the interest rate calculation.
  • Type of annuity. This refers to whether the annuity is an ordinary annuity that pays at the end of a period, such as the last day of the month, or annuity due that pays at the outset of a period, such as the first day of the month.

Because there are two types of annuities (ordinary annuity and annuity due), there are two ways to calculate present value.

Here are the key components of the formula:

  • P = Present value of the annuity
  • PMT = Total of each annuity payment
  • r = Interest rate, also known as discount rate (%)
  • n = Total number of payment periods

Here’s how the formula looks if you’re applying it to an ordinary annuity (also called a deferred annuity):

P = PMT [(1 – [1 / (1 + r)^n]) / r]

Jack is expecting $7,500 for 20 periods from an ordinary annuity with an interest rate of 6%. In Jack’s situation, he’d use this formula:

P = 7,500 [(1 -[1 / (1 + .06)^20]) / .06]

After Jack does the math, he’d come up with a present value of $86,024.41.

The formula looks slightly different if you’re applying it to an annuity due:

P = (PMT [(1 – [1 / (1 + r)^n]) / r]) x (1 + r)

Jill is expecting $7,500 for 20 periods in an annuity due with an interest rate of 6%. In Jill’s situation, she’d use this formula:

P = (7,500 [(1 – [1 / (1 + .06)^20]) / .06]) x (1 + .06)

After Jill does the math, she’d come up with a present value of $91,185.87.

What Is the Time Value of Money?

Something to keep in mind when determining an annuity’s present value is a concept called “time value of money.” With this concept, a sum of money is worth more now than in the future.

This has to do with how inflation chips away at value. Due to inflation, $1,000 today is worth more than what that same $1,000 will be worth in 10 years.

“Essentially, a sum of money’s value depends on how long you must wait to use it; the sooner you can use it, the more valuable it is,” Harvard Business School says.

Since an annuity’s present value depends on how much money you expect to receive in the future, you should keep the time value of money in mind when calculating the present value of your annuity.

What Is the Future Value of an Annuity?

The future value of an annuity refers to how much money you’ll get in the future based on the rate of return, or discount rate.

The effect of the discount rate on the future value of an annuity is the opposite of how it works with the present value. With future value, the value goes up as the discount rate (interest rate) goes up.

An annuity’s future value is also affected by the concept of “time value of money.” Due to inflation, the $500 you expect to receive in 10 years will have less buying power than that same $500 would have today.

How to Calculate the Future Value of an Annuity

As with the present value of an annuity, you can calculate the future value of an annuity by turning to an online calculator, formula, spreadsheet or annuity table.

You’ll need this information:

  • Payment amount. The amount of each annuity payout.
  • Interest rate. The annuity interest rate, or discount rate, per period.
  • Number of payout periods. The number of periods when you’ll receive payouts.
  • Type of annuity. This refers to whether the annuity is an ordinary annuity that pays at the end of a period, such as the last day of the month, or annuity due that pays at the outset of a period, such as the first day of the month.

The key components of the formula are:

  • FV = Future value of annuity
  • PMT = Amount of each annuity payout
  • r = Interest rate, also known as discount rate (%)
  • n = Number of payment periods

Here’s how the formula looks if you’re applying it to an ordinary annuity (also called a deferred annuity):

FV ordinary = PMT x [ ([1 + r]^n – 1) / r]

Jack expects 30 quarterly payouts of $500 each on an ordinary annuity with an annual interest rate of 6%. In Jack’s situation, he’d use this formula:

FV ordinary = 500 x [ ([1 + .06]^30 – 1) / 0.6]

After Jack does the math, he’d come up with a future value of $39,529.09.

The formula looks a little different if you’re applying it to an annuity due:

FV due = PMT x [ ([1 + r]^n – 1) x (1 + r) / r]

Jill expects 30 quarterly payouts of $500 each on an annuity due with an annual interest rate of 6%. In Jill’s situation, she’d use this formula:

FV due = 500 x [ ([1 + .06]^30 – 1) x (1 + .06) / .06]

After Jill does the math, she’d come up with a future value of $41,900.84.

Why Do You Need to Know Present and Future Value?

Certified financial planner Lance Dobler, a senior regional director and vice president on TIAA’s private asset management team, says that calculating present and future values for an annuity can help give you peace of mind about your financial future.

“Knowing these numbers is simple in theory but very often overlooked in practice,” Dobler says. “Without up-to-date, dynamic forecasting, many investors fail to properly examine their investments and fail to include guaranteed lifetime income options that will help provide retirement security.”

This could mean delaying retirement or adjusting retirement income goals, Dobler says. “You also may need to either take on additional risk as you near retirement or, conversely, you may not be able to take on additional risk when trying to maximize legacy and philanthropic goals leading up to and into retirement.”

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The views and opinions expressed herein are the views and opinions of the author and do not necessarily reflect those of Nasdaq, Inc.



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