Question

Enrique borrowed $\backslash (23,500$to buy a car. He pays his uncle $2\%$interest on the $\backslash )4,500$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.)

Short answer

Enrique has to pay average interest of$\$2275.$

Step-by-step solution

Step 1. Given Information   

The cost of a car is $\$23500$and he pays his uncle $2\%$interest on $\$4500$he borrowed from him and he pays the bank$11.5\%$interest on the rest. We have to find the average interest rate he pay on the total$\$23500.$

Step 2. Translate into an equation

Let xbe average interest.

Now, he pays $2\%$interest to his uncle on the $\$4500$he borrowed from him so, $\left(4500\times \frac{2}{100}\right).$

Then he pays the bank $11.5\%$interest on the rest so, role="math" $\left[\left(23500-4500\right)\times \frac{11.5}{100}\right].$

So, the equation is

role="math" localid="1647263650133" $x=\left(4500\times \frac{2}{100}\right)+\left(19000\times \frac{11.5}{100}\right)$

Step 3. Solve the equation 

By proceeding with the equation we get,

$$\begin{gathered} x=\left(4500\times \frac{2}{100}\right)+\left(19000\times \frac{11.5}{100}\right) \\ x=90+2185 \\ x=2275 \end{gathered}$$

So, Enrique has to pay the average interest of$\$2275.$