15 Percent Annual Interest

Date: 8/24/96 at 0:1:51
From: Anonymous
Subject: Formula for Compound Intrest

I want to calculate the amount of money I will have in 29 years if I 
put $120 per month into an account that will earn 15 percent interest 
per year.

I have a TI 83 calculator and I do not agree with the answer that I am 
getting.  I believe that I must be doing something wrong.

If you can supply a formula for this problem it would be greatly 
appreciated.

Thank you,
Jim Eastman

Date: 8/25/96 at 15:54:45
From: Doctor Robert
Subject: Re: Formula for Compound Intrest

The answer, of course, depends on how often your interest is 
compounded. Since you keep adding to the principal, this is an 
annuity. The formula for the future value of an annuity is

  S = P((1+i)^n-1)/i  

where P is the amount invested each compounding period, i is the 
interest rate per period, and n is the number of periods.

If your money is invested at 15 percent annually, then you have 29 
compounding periods. n = 29, P = 12(120) and i = 0.15 (which seems 
pretty high).  

Mathematica says:

   12.0*120.0*((1.15)^29 - 1)/0.15 = 543124.

So S is approximately 543 thousand dollars.

If the interest is compounded monthly then n = (29)(12), i = .15/12,  
and P = 120.  Then S is approximately 714 thousand dollars. 

Does your TI-83 agree with these?

-Doctors Robert and Ken,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/