Ordinary annuities are fixed-size investments that yield interest-bearing payments over a preset period of time. They’re typically issued as an insurance contract by insurance companies. The first periodic payment, or “PMT,” is received at the end of a specified period of time.
An annuitant, or holder of an annuity, can calculate the present value of an annuity, the future value of an ordinary annuity and/or regular payment amounts in a few ways. One requires some math. The other much easier option is to let a website do the work for you.
Ordinary Annuity vs. Annuity Due
Annuities tend to be used as retirement planning tools. There are different types of annuities. A “fixed annuity” is simply one that guarantees the holder a fixed rate of return on their investment during a set period of time or payment period.
An annuity due differs from an ordinary annuity in that its cash flows are paid out at the beginning of a prescribed time period, according to Saylor Academy. The payout of an annuity due is typically superior to that of an ordinary annuity because investments are immediate rather than deferred, resulting in an extra period of interest.
These calculations pertain to ordinary annuities.
Calculate the Yearly Annuity Payment
First, determine one of the three variables of interest. We'll call these variables PV, FV and p:
- The investment’s present value
- The investment’s future value and/or
- The investment’s periodic payment.
Now determine the rate of interest at which the annuity will be invested. Call this variable i, for interest. Interest is usually expressed as an annual rate.
Determine the number of years for which the annuity will make payments. Call this number n, for the number of payments.
Calculate the yearly annuity payment using this formula:
p = [PV x i]/[1-(1+i)^-n]
You’ll receive a yearly payment of [25,000 x .10]/[1-(1+.10)^-5] = $6,594.94 if the present value of the annuity is $25,000 at a 10 percent annual rate of interest and it will pay for five years.
Calculate Future Value
You can calculate the future value of the annuity using this formula:
FV = p x [(1 + i)^n – 1]/i
The future value will be 6,594.94 x [(1.1)^5 – 1]/.10 = $40,262.77 if the annuity will pay $6,594.94 per year for five years at a 10 percent annual rate of interest.
Calculate Present Value
Annuity.org defines present value as the current cash value of all payments you haven't received yet based on the annuity's discount rate or rate of return. Picture it like a seesaw: The present value will be higher when the rate of return is on the low end.
Calculate the present value of the annuity using this formula:
PV = p x [1 – (1 + i)^-n]/i
The present value is 6,594.94 x [1 – (1.1)^-5]/.10 = $25,000 if the annuity will pay $6,594.94 per year for five years at a 10 percent annual rate of interest.
The Final Calculation
Finally, the present value and the future value can be calculated from each other:
FV = PV x (1 + i)^n
So 25,000 x (1.1)^5 = $40,262.77 and PV = FV x (1 + i)^-n works out to 40,262.77 x (1.1)^-5 = $25,000.
Calculating "n" is more difficult, but it can be accomplished using the logarithmic reduction of the annuity formula. Fortunately, "n" is almost always given to you. On the other hand, "i" is actually impossible to calculate explicitly, so you’ll have to use a financial calculator or manually interpolate to estimate it if you want to calculate the implicit interest rate of an annuity given the investment and payment amounts. Like "n," "i" will almost always be given as well.
Calculating the Easier Way
Annuity.org indicates that you can do these calculations using Excel, and it provides an image of a spreadsheet example. You can either do the math manually or let Excel do it for you.
Perhaps the easiest way to calculate an ordinary annuity value is to visit a site such as the American Association of Individual Investors. AAII provides an annuity calculator for pinning down the present value of an annuity. It’s designed to adjust for compounding interest and compounding frequency.
Using it begins with selecting your payment term, such as annually, quarterly or monthly. Then tell the calculator what you want to solve for. One of the options is the present value.
Enter the yearly amount of the annuity, the number of years of the annuity and the annual interest rate. Click on "calculate" and you'll have your answer.
The tool can also tell you the interest, the number of years or the payment amount if this is the information you're looking for. Future value calculators are available online as well.
- Calculating n is more difficult, although it can be done using the logarithmic reduction of the annuity formula. Fortunately, n is almost always given to you. On the other hand, i is actually impossible to calculate explicitly, so if you want to calculate the implicit interest rate of an annuity given the investment and payment amounts, you’ll need to use a financial calculator or manually interpolate to estimate it. Like n, i will almost always be given as well.
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