college algebra

Question

Kevin invested part of his $5,000 bonus in a certificate of deposit that paid 2% annual simple interest, and the remainder in a mutual fund that paid 4% annual simple interest. If his total interest for that year was $190, how much did Kevin invest in the mutual fund?

Answer 1

Hello, thank you for taking the time to post your question!

The key on this type of question is finding a way to relate the variables to one another in an algebraic expression. On this one we have

x + y = 5000         because we know that he invested $5000 in total between the two assets

0.02x + 0.04y = 190     because between the 2% return and 4% return he earned $190 in total interest

I would substitute in the first expression into the second and the solve for the underlying value of “y” … when I do that I get y = 4500, meaning that x = 5000 – 4500 = 500

So he invested $4500 in the mutual fund and then the remaining $500 in the certificate of deposit

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

190/5000 = 19/500 = .038 = 3.8 % interest, within .2% of 4% and within 1.8% of 2%

18/2 = 9. Kevin invested 9 times as much at 4% as at 2%

9x = (5000-x)

10x = 5000

x = $500 invested at 2%

and 9(500) = $4,500 invested at 4%

or another method: solve the following equation

adding the interest at each rate to get the total interest

..04X + .02(5000-X = 190

(.04-.02)X = 190 -100 = 90

X = 90/.02 = $4500 at 4%

5000-4500 = $500 at 2%