Present Value of an Annuity
The present value of an annuity is based on the concept of the time value of money. The time value of money means that money is worth more the sooner you have it. Payments that are scheduled to be received in the future are worth less today because of the uncertainty of future economic conditions. Current payments have more value because they can be invested in the meantime.
The present value of an annuity is the current value of the future payments that the annuitant will receive, given a specified rate of return. The present value measures the current cash value of all of the future payments that the annuitant will receive.
The present value calculation is useful in determining whether the annuitant will receive more money by taking an immediate lump sum or spreading out annuity payments over a longer period of time.
How to Calculate the Present Value of an Annuity
There is a formula that can be used to calculate the present value of an annuity. The formula is as follows:
PV= PMT x ((1 – (1 + r)^ – n) / r)
– PMT= the periodic payment
– r= the interest rate per period
– n= the total number of periods
The following are two examples of scenarios involving an annuity and the accompanying present value calculation:
Jessica is considering buying an ordinary annuity that will pay $45,000 per year for 10 years with an interest rate of 6%. She calculates the present value of her annuity with the following calculation:
$45,000 x ((1– (1+ 0.06)^ -10) / 0.06) = $331,203.92
Robert was recently the plaintiff in a lawsuit and he is going to be paid settlement money. Robert must decide whether he wants to receive the settlement money as a lump sum or in the form of a structured settlement annuity. He has the option to receive a structured settlement annuity that will pay $50,000 per year with a 5% interest rate for the next 20 years, or take a $630,000 lump sum payment. Robert is going to decide which option to take based on which choice will give him the most value. The following present value calculation will allow Robert to see how much money he will receive over time from a structured settlement:
$50,000 x ((1– (1+ 0.05)^ -20 / 0.05) = $623,110.52
Based on this calculation, Robert opts to receive his settlement money as a lump sum because he will receive $630,000 with that option, as opposed to only $623,110.52 with a structured settlement.
Special thanks in preparing this summary of “What is The Present Value of an Annuity?” goes to Bob Carlson, leader of the Retirement Watch advisory service and chairman of the Board of Trustees of Virginia’s Fairfax County Employees’ Retirement System with more than $4 billion in assets.