A Loan That Compounds Interest Monthly Has An Ear Of 14.40 Percent. What Is The Apr?

 To calculate the Annual Percentage Rate (APR) from the Effective Annual Rate (EAR), we can use the formula:

$𝐴𝑃𝑅={(1+\frac{𝐸𝐴𝑅}{𝑛})}^{𝑛}-1$

Where:

• $𝐸𝐴𝑅$ is the Effective Annual Rate (in decimal form),
• $𝑛$ is the number of compounding periods per year.

Given that the loan compounds interest monthly ($𝑛=12$) and the EAR is $14.40\mathrm{\%}$ (or $0.144$ in decimal form), we can plug these values into the formula:

$𝐴𝑃𝑅={(1+\frac{0.144}{12})}^{12}-1$

$𝐴𝑃𝑅={(1+0.012)}^{12}-1$

$𝐴𝑃𝑅=(1.012{)}^{12}-1$

$𝐴𝑃𝑅=1.126825-1$

$𝐴𝑃𝑅\approx 0.126825$

To express the APR as a percentage, we multiply by $100$:

$𝐴𝑃𝑅\approx 0.126825\times 100\mathrm{\%}$

$𝐴𝑃𝑅\approx 12.6825\mathrm{\%}$

So, the Annual Percentage Rate (APR) for the loan is approximately $12.6825\mathrm{\%}$.