# Periodic withdrawal formula

by Gablar16
Tags: formula, periodic, withdrawal
 Sci Advisor HW Helper P: 3,146 Of course there are formulas to calculate the amounts but you can derive them easily enough. Just break it down into manageable chunks: The last payment made accrues interest for exactly 1 month so its value at the end of the month is $(1+i)p$ where i is the periodic interest rate and p is the payment. The next to last payment accrues interest for 2 months so its value is $(1+i)^2 p$ and so forth. The sequence of values is simply a geometric series with which you should have no difficulty finding the sum. You can develop a similar series for the withdrawal part of your annuity.