Question

Paul has $20,000 to invest. His intent is to earn 11% interest on his investment. He can invest part of his money at 8% interest and part at 12% interest. How much does Paul need to invest in each option to make get a total 11% return on his $20,000?To earn full credit please identify your variables and expressions you will be using to solve the problem. Show all work/calculations and thinking.

Answer 1

Answer:

Step-by-step explanation:

Total amount of money invested = $20000

Interest on the $20000 investment = (11/100) x 20000

Interest on the $20000 investment = $2200

Let the amount invested with 8% interest be m

Interest on the 8% investment = (8/100) x m

Interest on the 8% investment = 0.08m

Let the amount invested with 12% interest be n

Interest on the 12% investment = (12/100) x n

Interest on the 12% investment = 0.12n

The total amount invested is $20000

m + n = 20000.............(1)

Total interest is $2200

0.08m + 0.12n = 2200........(2)

Make m the subject of the formula in equation (1)

m = 20000 - n.............(3)

Substitute equation (3) into equation (2)

0.08(20000 - n) + 0.12n = 2200

1600 - 0.08n + 0.12n = 2200

0.04n = 2200 - 1600

0.04n = 600

n = 600/0.04

n = 15000

Substitute n = 15000 into equation (3)

m = 20000 - 15000

m = 5000

The amount Paul invested at 8% interest i