Question

8. A total of $54,250 is be invested, part at 5.370% annual interest and the rest at 6.720% annual interest.

How much is invested at each rate to provide an annual interest income of $3,100?

Answer 1

Approximately $41,296.30 is invested at 5.370% annual interest, while the rest, approximately $12,953.70, is invested at 6.720% annual interest.

Step-by-step explanation:

Let's use the method of solving a system of linear equations to find out how much is invested at each interest rate.

Let's say the amount invested at 5.370% annual interest is x dollars. The remaining amount invested at 6.720% annual interest would be $54,250 - x dollars.

Now, let's set up the equation:

x * 0.0537 + (54250 - x) * 0.0672 = 3100

0.0537x + 3657 - 0.0672x = 3100

-0.0135x + 3657 = 3100

-0.0135x = -557

x = -557 / -0.0135 ≈ 41296.3

Therefore, approximately $41,296.30 is invested at 5.370% annual interest, and the rest, approximately $12,953.70, is invested at 6.720% annual interest.