Phyllis invested $12,000, a portion earning a simple interest rate of 4 1 2 % per year and the rest earning a rate of 4% per year.

Question

Phyllis invested $12,000, a portion earning a simple interest rate of
4
1
2
%
per year and the rest earning a rate of 4% per year. After one year the total interest earned on these investments was $517.50. How much money did she invest at each rate? 

and also for 4% 

 

Answer 1

Suppose Phyllis invested X dollars at the 4.5% rate. Then she invested ($12,000 - X) dollars at the 4% rate.

Write the equation for the interest she received on both of those investments:

 

X * 4.5% + ($12,000 - X) * 4% = $517.50

 

Solve this equation for X:

 

X * 4.5% + $480 - X * 4% = $517.50

X * 0.5% = $37.50

X = $7,500

 

Then ($12,000 - X) = $12,000 - $7,500 = $4,500

 

So, Phyllis invested $7,500 at 4.5% and $4,500 at 4%.