Present Value of an Annuity Due

Here is the formula for the present value of an
Annuity Due (payments at beginning):

PV_AnnDue = R · [

1 - ( 1 + i )^{- n}
----------------
i

] · ( 1 + i )

PV is the present value of the annuity due,
R is the amount of the regular payment per period,
n is the total number of payment periods
(number of payment periods per year * number of years,
i is the interest rate per period
(annual interest rate written as a decimal ÷ number of periods per year )

Example: Suppose I withdraw $200 per month at 4.5% annual interest for 11 years from an account with payments at the beginning of each month. How much will the account need to have in it to be able to do this?

This is how you would put the values into the formula to work it out with a calculator:

PV = 200 · [

1 - ( 1 + .045 / 12 )^{- (12 * 11)}
--------------------------------
(.045 / 12)

] · ( 1 + .045 / 12 )

PV = $20,870.75

If you enter the above numbers correctly on a calculator, you should get an answer for PV of $20,870.75

Try entering those numbers in the appropriate spaces in the box above, press the "Calculate" button, and see if you get the correct answer. You can use this calculator to practice problems and make sure you are evaluating them correctly on your calculator.

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Created on ... Dec 1, 2009

Last updated on ... Dec 1, 2009