Quarterly Interest

Date: 6/3/96 at 18:16:4
From: GEORGE DICKENSON
Subject: Compound Interest

How long will it take for a sum deposited in a savings account to 
double if it is paid 6 percent interest compounded quarterly?

Date: 6/14/96 at 0:56:23
From: Doctor Brian
Subject: Re: math problems

I assume that the 6 percent interest is an annual figure.  That means 
that only 1.5 percent interest is found each quarter.  You find the 
interest by multiplying the principal by .015.  However, we'd need to 
add that to the original amount.  Multiplying the principal by 1.015 
has that exact effect - the .015 part measures the interest gained, 
while the 1 part keeps track of the original amount.

So every time we do interest, we essentially multiply our old amount 
by 1.015.  Two calculations would be like multiplying by 1.015 twice.  
This is the equivalent of multiplying by

(1.015)^2 = 1.030225.  

We need to know how many times we'd have to multiply by 1.015 to gain 
the net effect of multiplying by 2 (doubling the amount).

So the equation is (1.015)^x = 2.

This is then a log problem, because 

x = log, base 1.015, of 2.

The change-of-base formula lets us solve

x = (log 2)/(log 1.015)

for any base.  x = 46.5555.  
So we have to compute interest 47 times to double our amount.  Since 
we do interest four times a year, this brings us to almost 12 years.

-Doctor Brian,  The Math Forum
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