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### 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

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/
```
Associated Topics:
High School Interest

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