Interest rates

Question

The annual interest on a $9000 investment exceeds the interest earned on a $6000 investment by $135. The $9000 is invested at a 0.5% higher rate of interest than the $6000. What is the interest rate for each investment?

Answer 1

First, just for simplicity let's assume the interest rates X and Y on $9,000 and $6,000 investment written as decimals (later we will convert them to % by multiplying each by factor 100). Based on this assumption, the math problem can be written as following system of 2 linear equations with 2 unknown variables X and Y:

 

9000X=6000Y+135

X=Y+0.005

 

In canonical form:

 

9000X-6000Y=135

X-Y=0.005

 

This system of equations could be solved manually, or using online equations solver (http://examn8.com/SystemOfEquations.aspx)

 

The answer is X=0.035 and Y=0.3 corresponding to X=3.5% (the rate on $9,000 investment) and Y=3% (the rate on $6,000 investment).

 

Hope this may help.