Amount of Interest Earned in a Year

Date: 11/28/95 at 14:17:17
From: Anonymous
Subject: hard math

If Li Fong had earned one fourth of a percent more in annual interest
on an investment, the interest for one year would have been $45 greater. 
How much did she invest at the beginning of the year?

Date: 11/28/95 at 15:54:36
From: Doctor Ken
Subject: Re: hard math

Hello there!

I think that the hardest part of this question is figuring out the 
equation you have to solve.  Essentially, that means translating the 
words in the problem into mathematical symbols so that you can 
work with them.  I'll help you through it:

One percent is 1/100, so 1/4 of 1 percent is 1/4 * 1/100 = .25 * .01
                                                         = .0025

So let X equal the amount of money Li Fong invested, and let P be the 
percentage rate (something like 1.04 for 4% or something like that).  
Then the first part of the equation is this:

 X(P + .0025)

That's 1/4 of a percent more interest.  Then the whole phrase "the 
interest for one year would have been" just means "=".  So we have

 X(P + .0025) = XP + 45

because XP is the actual amount she ended up with at the end of a year, 
and raising the interest would have made that $45 more.  Now that you 
have that equation, you can just solve for X!

Good luck.

-Doctor Ken,  The Geometry Forum