Your bank has agreed to grant you a discount loan with an APR of 5.25%.If you need $5,000 today,the loan is to be repaid in full in one year,and the total interest to be paid is $277,what is the EAR of the loan?

Question

Quizplus · Accepted Answer

To calculate the EAR, we need to use the formula:

EAR = (1 + APR/m)^m - 1

where APR is the annual percentage rate, and m is the number of compounding periods per year.

In this case, APR = 5.25% and the loan is to be repaid in full in one year, so m = 1.

To find the discount loan's EAR, we need to solve for (1 + APR/m)^m:

(1 + APR/m)^m = 1 + EAR

(1 + 0.0525/1)^1 = 1 + EAR

1.0525 = 1 + EAR

EAR = 1.0525 - 1 = 0.0525 = 5.25%

However, the problem tells us that the total interest to be paid is $277. This means that the amount of the loan that will actually be received is $5,000 - $277 = $4,723.

Using this amount, we can calculate the true APR of the loan:

$4,723 = $5,000/(1 + APR/1)^1

(1 + 0.0525)^1 = $5,000/$4,723

1.0525 = 1.0634

APR = (1.0634 - 1) x 100% = 6.34%

Now we can use this true APR value to calculate the EAR:

EAR = (1 + 0.0634/1)^1 - 1 = 0.054 = 5.54%

Therefore, the best choice is B, with an EAR of 5.54%.

Your Bank Has Agreed to Grant You a Discount Loan