Formula for 8 Percent Interest

Date: 5/31/96 at 22:5:0
From: Mark Kelly
Subject: A formula needed

I need a formula for this problem:  I put $15 a month into a savings 
account.  At the end of each year I get 8% interest.  I repeat this 
again until three years has gone.  

Here are the answers if you work it out the long way (including 
8 percent interest).

First year:  194.40
Second year: 404.352
Third year:  631.10

I have tried and tried, and can't get a formula for it.  

A formula I want is something like this for a lump sum.

A = P (1 + r / n ) power of (nt)

Key:
A = Money accumulated
P = Principal amount
r = Annual rate
n = Number of compounding periods per year
t = Number of years.

Thank you.

Date: 6/1/96 at 1:17:58
From: Doctor Ken
Subject: Re: A formula needed

Hello -

Here are a couple of hints on how to come up with a formula.  You can 
kind of build the formula exactly the same way you did these "the long 
way."  One thing you can do to simplify this problem is to notice that 
everything would work out the same if you put in all the money for a 
year at the same time (as long as it's before the interest is given to 
you!).  So you don't really need to think about putting in $15 a 
month, you can just thing about it as $15 x 12 = $180 per year.

So let's try starting to build a formula.  Instead of simplifying 
after each step, let's just leave all the terms dangling all over the 
place, like this:

1 year:   1.08*180
2 years:  1.08*(1.08*180 + 180)
3 years:  1.08*(1.08*(1.08*180 + 180) + 180)

Does this help you figure out the problem?  Please feel free to write 
back if you work on it a while and you're still confused!

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