Question

.

Paul has $35000 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 14% interest. How much does Paul need to invest in each option to make get a total 11% return on
his $35000?
Investing for 8% return: $
9
Investing for 14% return: $
B

Answer 1

• $17,500 at 8%
• $17,500 at 14%

Explanation:

The fraction that needs to be invested at the higher rate is ...

(11% - 8%)/(14% -8%) = 3%/6% = 1/2

Half the money should be invested at each of the rates:

$17,500 for 8% return

$17,500 for 14% return.

_____

If you let x represent the amount at the higher rate, then the total return is ...

14%x + 8%(35000 -x) = 11%(35000)

(14% -8%)x = (11% -8%)(35000) . . . . subtract 8%·35000

x = (11% -8%)/(14% -8%)×35000 . . . . divide by the coefficient of x

Note that this formula is exactly the one we started with, above.