To find the APR from the given EAR of 14.40% that compounds monthly, you use the reverse compounding formula and then multiply the monthly rate by 12 to get the annual rate. The APR is approximately 13.36%, which is closest to option b. 13.59%, after rounding.
To convert the Effective Annual Rate (EAR) to the Annual Percentage Rate (APR), you need to use the following formula:
APR = (1 + EAR)^(1/n) - 1, where n is the number of compounding periods per year.
For a loan with an EAR of 14.40% that compounds interest monthly, the formula becomes:
APR = (1 + 0.144)^(1/12) - 1, APR = (1.144)^(1/12) - 1, APR = 1.01113 - 1, APR = 0.01113.
Converting this to percentage gives:
APR = 0.01113 × 100, APR = 1.113% per month.
To find the yearly rate, you multiply by 12:
APR = 1.113% × 12, APR = 13.3596%.
This means the closest APR to your EAR of 14.40% would be 13.36%, which corresponds to option b. 13.59%, considering that we round it to two decimal places.
to convert the EAR to the APR for a loan that compounds interest monthly, you apply the compounding formula in reverse and then annualize the monthly rate by multiplying by 12.