MATH HW QUESTION

Question

Jack has $12,000 to invest and wants to earn 7.5% interest per year. He will put some of the money into a savings account that earns 4% per year and the rest into a CD account that earns 9% per year. How much money should he put into each account?

Answer 1

A substitution should work here

Jack would simply invest x amount at one of the rates

Jack would invest 12000 - x at the other rate

Together these should add up to the earnings expected for 12000 at 7.5%

Convert the rates into decimals for the calculations

So we have as a set up

.09x + .04(12000 - x) = .075(12000)

.09x + 480 - .04x = 900

Combining like terms

.09x - .04x = 900 - 480

.05x = 420

Divide both sides by .05

x = 8400

Just plug this value back into the original set up

we have

.09(8400) = 756

.04(12000 - 8400) = .04(3600) = 144

And finally

756 + 144 = .075(12000)

756 + 144 = 900

Jack would invest $8400 at 9% and $3600 at 4%

I hope you find this useful and please send me a message if you have any questions

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