Question

Bank Monash quotes the interest rate on loans as 5% per annum continuously compounded. The interest is actually paid monthly on a $3752 loan. What is the interest payment (in $) of this loan per month?

p.s That's the whole problem. It didn't provide any info about the duration.

Answer 1

First, we compute the effective annual rate (EAR) of the loan.

EAR = e^rt - 1 (where r = annual rate of interest, and t = time in years)

EAR = e^0.05*1 - 1

EAR = 5.1271%

Next, we calculate the annual interest rate (r) such that, with monthly compounding, the EAR equals 5.1271%

EAR = (1 + (r/n))ⁿ - 1 (where n = number of compounding periods per year)

5.1271% = (1 + (r/12))¹² - 1

r = ((1 + 5.1271%)^1/12 - 1) * 12

r = 5.0104%

Monthly interest payment = loan amount * r / 12

Monthly interest payment = $3752 * 5.0104% / 12

Monthly interest payment = $15.67