What Is The Effective Annual Interest Rate On A 9% Apr Automobile Loan That Has Monthly Payments?

 To calculate the effective annual interest rate (EAR) on a loan with monthly payments, you can use the following formula, known as the Effective Annual Rate formula:

$\text{EAR}={(1+\frac{𝑟}{𝑛})}^{𝑛}-1$

Where:

• $𝑟$ is the nominal annual interest rate (APR) expressed as a decimal.
• $𝑛$ is the number of compounding periods per year.

For a loan with monthly payments, the APR (nominal annual interest rate) is 9%, and since there are 12 months in a year, $𝑛=12$.

First, convert the APR from a percentage to a decimal: $𝑟=\frac{9}{100}=0.09$.

Then plug the values into the formula:

$\text{EAR}={(1+\frac{0.09}{12})}^{12}-1$

$\text{EAR}={(1+\frac{0.09}{12})}^{12}-1$

$\text{EAR}={(1+0.0075)}^{12}-1$

$\text{EAR}={\left(1.0075\right)}^{12}-1$

$\text{EAR}=1.093806-1$

$\text{EAR}=0.093806$

To express the EAR as a percentage, multiply by 100:

$\text{EAR}=0.093806\times 100\mathrm{\%}$

$\text{EAR}=9.3806\mathrm{\%}$

So, the effective annual interest rate on a 9% APR automobile loan with monthly payments is approximately 9.38%.