How to Calculate the Present Value of an Annual Annuity
An annuity can be defined as a series of equal payments that occur evenly over a given time period. The most common type of annuity is a lease or rental payment. Finding the present value can be valuable if you wish to exchange or sell future payments for an upfront price. It's a simple matter to grasp an overview of the calculation process of the present value of an annual annuity.
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Things You'll Need
- Amount of each payment
- Timing of each payment (at the beginning or end of the cycle)
- Discount rate per period
Instructions
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How to Calculate the Present Value of an Annuity
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1
Determine what kind of annuity you have. Annuities that pay at the end of a period are referred to as "ordinary," while annuities which occur at the beginning of each period are referred to as an "annuity due."
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2
Calculate the present value of an ordinary annuity (PVoa) at the end of each period. This is also known as an ordinary annuity. The calculation is: PVoa = PMT [(1 - (1 / (1 + i)n)) / i], where "PMT" equals payment, "n" equals the number of periods and "i" equals the interest rate.
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3
If the amount you invest today is 6 percent compounded annually so that you can take out $5,000 at the end of each year for the next 5 years, the operative word is "end." Using the calculator for an ordinary annuity, the payment (PMT) would be $5,000; the interest rate is .06, and the period (n) is 5 (see link in Resources). The answer is $21,061.82.
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Calculating the present value of an annuity due (PVad) is identical to an ordinary annuity except that the payment will occur at the beginning of each period. The calculation is: PVad = PVoa (1+i).
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As an example, assume the same variables as we did for an ordinary annuity. That is, the discount rate is 6 percent compounded annually with a payment of $5,000 and the number of periods is 5 years. Plugging this into the equation or the calculator for PVad listed in Resources, the answer is $22,325.53.
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For clarity, calculate the difference between PVoa and the PVad. The difference is $1,263.71. It is the difference between the present value of an ordinary annuity due at the end of each period and the present value of those same cash flows when the annuity is due at the beginning of a period. In this case, the difference is worth $1,263.71 over a 5-year period.
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