# Formula for Compound Interest

1. Jan 28, 2006

### pdunn

Hello, I wanted to know is there a formula for compound interest when making additional payments. i.e. I make payments of $500 ever year for 5 years and NOT just$2500 once for the 5 year term.

The current way I am calculating the result is using Compound Interest of initial payment for one year, then use that value as the new payment plus \$500 for one year. I continue until 5 years have been reached. Is there a simplier and probably correct way to do this?

Thank you,
P

2. Jan 28, 2006

### shmoe

You can look up "annuity", but you can derive the formula you need if you know a little about geometric series.

Suppose your money grows by r per year, that is you have 500*r a year after your first payment. After 5 years, this first payment becomes 500*r^5. The second payment accumulates 4 years of interest is now at 500*r^4, and so on. At the end of 5 years (and 5 payments total) you have:

500*r^5+500*r^4+500*r^3+500*r^2+500*r=500*r*(r^4+...+1)=500*r*(r^5-1)/(r-1)