An executive invests $22,000, some at 7% and some at 6% annual interest. If he receives an annual return of $1,420, how much is invested at each rate?

Question
Algebra foundations
asked 2020-11-26
An executive invests $22,000, some at 7% and some at 6% annual interest. If he receives an annual return of $1,420, how much is invested at each rate?

Answers (1)

2020-11-27
If x is invested at 7%, then 22000−x is invested at 6%.
The annual return is $1420 so we can write:
\(\displaystyle{0.07}{x}+{0.06}{\left({22000}−{x}\right)}={1420}\)
Solve for x:
\(\displaystyle{0.07}{x}+{1320}−{0.06}{x}={1420}\)
\(\displaystyle{0.01}{x}+{1320}={1420}\)
\(\displaystyle{0.01}{x}={100}\)
\(\displaystyle{x}=\frac{{100}}{{0.01}}\)
\(\displaystyle{x}={10000}\)
So, the executive invested $10,000 at 7% and $12,000 at 6%.
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