Question

Equal amounts are invested at 2%, 7%, and 9% annual interest. If the three investments yield a total of $792 annual interest, find the total investment.

Answer 1

`\large \boxed{\$13 200}`

Explanation:

The formula for simple interest I is

I = Prt, where

P = the principal (amount invested)

r = the interest rate per period and

n = the number of periods

In this problem, the interest rate is annual, so n = 1.

We must write the interest rate as a decimal fraction.

Let x = amount of each investment. Then

0.02x = interest at 2 %

0.07x = interest at 7 %

0.09x = interest at 9 %

0.18x = total interest

`\begin{array}{rcl}0.18x & = & 792\\x & = & (792)/(0.18)\\& = & 4400\\\end{array}\\\text{Each investment was \$4400.}\\\text{The total investment was 3$* \$4400$ or $\large \boxed{\mathbf{\$13 200}}$}`