Question

Phyllis invested $12,500, a portion earning a simple interest rate of

4 1/5%
per year and the rest earning a rate of 4% per year. After one year the total interest earned on these investments was $518.00. How much money did she invest at each rate

Answer 1

Let x be the amount invested at 4 1/5% interest rate. Then, the amount invested at 4% rate would be $12,500 - x.

The interest earned on the x amount at 4 1/5% interest rate can be calculated as x * 4.2 / 100 * 1.
And the interest earned on the ($12,500 - x) amount at 4% rate can be calculated as ($12,500 - x) * 4 / 100 * 1.

The total interest earned after a year is $518, so we can set up the following two equations:

x * 4.2 / 100 * 1 = x * 0.042 * 1

($12,500 - x) * 4 / 100 * 1 = ($12,500 - x) * 0.04 * 1

Adding the above two equations, we get:

x * 0.042 * 1 + ($12,500 - x) * 0.04 * 1 = $518

Expanding and solving for x, we get:

x = $8470

So, Phyllis invested $8470 at 4 1/5% interest rate and $12,500 - $8470 = $4030 at 4% interest rate.