What Is The Apr On A Loan That Charges Interest At The Rate Of 1.4% Per Month?

To calculate the Annual Percentage Rate (APR) of a loan that charges interest at a monthly rate of 1.4%, you need to first convert the monthly interest rate to an annual rate and then apply it to the APR formula.

Here's the formula to convert the monthly interest rate to an annual rate:

$𝐴𝑛𝑛𝑢𝑎𝑙𝑅𝑎𝑡𝑒=𝑀𝑜𝑛𝑡ℎ𝑙𝑦𝑅𝑎𝑡𝑒\times 12$

Given that the monthly interest rate is 1.4%, we can calculate the annual rate as follows:

$𝐴𝑛𝑛𝑢𝑎𝑙𝑅𝑎𝑡𝑒=1.4\mathrm{\%}\times 12$

$𝐴𝑛𝑛𝑢𝑎𝑙𝑅𝑎𝑡𝑒=16.8\mathrm{\%}$

Now that we have the annual interest rate, we can use it in the formula to calculate APR. The formula for APR is:

$𝐴𝑃𝑅=\left(\frac{2\times 𝑛\times 𝑖}{𝐿+(𝑛+1)\times 𝑖}\right)\times 100$

Where:

• $𝑛$ is the number of payments per year (12 for monthly payments)
• $𝑖$ is the periodic interest rate (in decimal form)
• $𝐿$ is the loan amount

Given that $𝑛=12$ (for monthly payments), $𝑖=0.014$ (1.4% in decimal form), and let's assume $𝐿=\mathrm{\$}1,000$ for simplicity, we can calculate the APR.

Substituting the values into the formula:

$𝐴𝑃𝑅=\left(\frac{2\times 12\times 0.014}{1000+(12+1)\times 0.014}\right)\times 100$

$𝐴𝑃𝑅\approx \left(\frac{0.336}{1000+0.014\times 13}\right)\times 100$

$𝐴𝑃𝑅\approx \left(\frac{0.336}{1000+0.182}\right)\times 100$

$𝐴𝑃𝑅\approx \left(\frac{0.336}{1000.182}\right)\times 100$

$𝐴𝑃𝑅\approx \left(\frac{0.336}{1000.182}\right)\times 100$

$𝐴𝑃𝑅\approx \left(\frac{0.336}{1000.182}\right)\times 100$

$𝐴𝑃𝑅\approx \left(\frac{0.000336}{1}\right)\times 100$

$𝐴𝑃𝑅\approx 0.0336\times 100$

$𝐴𝑃𝑅\approx 3.36\mathrm{\%}$

So, the APR on the loan with a monthly interest rate of 1.4% is approximately 3.36%.