Question

Liam borrowed a total of $35,000 to pay for college. He pays his parents 3% interest on the $8,000 he borrowed from them and pays the bank 6.8% on the rest. What average interest rate does he pay on the total $35,000? (Round your answer to the nearest tenth of a percent.)

Answer 1

5.9%.

Explanation:

The total amount of interest Liam pays to his parents is (0.03)8000=240.

The total amount of interest he pays to the bank is (0.068)(35000−8000)=1836.

So, Liam pays 240+1836=2076 in interest on the 35000 he owes, which is a rate of

207635000≈0.059,

or 5.9%.

Answer 2

The weighted average of the interest rates is ...

`(\$8000* 3\%+27000* 6.8\%)/(\$35000)=(\$240+1836)/(\$35000)\\\\=(2076)/(35000)\approx 5.9\%`

The average interest will vary with payments made, but as long as the entire balance is outstanding (and interest is not compounded), the average rate is about 5.9%.