Question

Enrique borrowed $23,500 to buy a car. He pays his uncle 2% interest on the $4,500 he borrowed from him, and he pays the bank 11.5% interest on the rest. What average interest rate does he pay on the total $23,500? (Round your answer to the nearest tenth of a percent.)

Answer 1

0.097 or 9.7%

Explanation:

Enrique pays 0.02(4,500)=90 in interest to his uncle.

He pays 0.115(23,500−4,500)=2,185 in interest to the bank.

The total amount of interest he pays is 2,185+90=2,275, which is a rate of

2,275/23,500≈0.097

or 9.7%.

Answer 2

He pays average 9.7% interest on the total $23,500.

Explanation:

Enrique borrowed total $23,500 to buy a car.

Suppose, he pays average
`x\%` interest on the total $23,500.

So, the total amount of interest will be:
`(23,500* x\%)= (23,500*(x)/(100))=235x` dollars.

He borrowed $4,500 from his uncle and pays 2% interest for this.

So, the amount of interest paid to his uncle
`=(4,500* 2\%)=(4,500* 0.02)= 90` dollars.

He borrowed the rest amount which is ($23,500- $4,500) or $19,000 from the bank and pays 11.5% interest for it.

So, the amount of interest paid to the bank
`=(19,000* 11.5\%)= (19,000* 0.115)=2,185` dollars.

Thus, the equation will be.........

`235x=90+2185\\ \\ 235x=2275\\ \\ x=(2275)/(235)=9.6808... \approx 9.7`

(Rounded to the nearest tenth)

So, he pays average 9.7% interest on the total $23,500.