Question

An actor invests some money at 5% simple interest, and $23,000 more than 3 times the amount at 6% simple interest. The total annual interest earned from the investment is $28,290. How much did he invest at each amount? Use the 6 step method.

Answer 1

He invested $117,000 at 5% interests and 3*117,000 + 23000 = $374,000 at 6% interests

Explanation:

Let's call x to the some money at 5% simple interest the actor invest. Then, he invested 3x + 23000 dollars at 6% simple interest.

At 5% simple interest, after one year he earned the following interests:

I = P*r*t

I = x*0.05

At 6% simple interest, after one year he earned the following interests:

I = (3x + 23000)*0.06 = 0.18x + 1380

The total annual interest earned from the investment is $28,290, then:

0.05x + 0.18x + 1380 = 28290

x = (28290 - 1380)/0.23

x = $117,000