Answer:
The effective interest will be 37.13 if the payments are monthly or 36.05 if the payments are quarterly.
Step-by-step explanation:
Let's evaluate the information given:
Amount of the loan = US$ 500
Duration of the loan = 3 months
Net amount received by Billie into her bank account = US$ 460
Interests for the loan = Amount of the loan - Net amount received into bank account
Interests for the loan = 500 - 460
Interests for the loan = US$ 40
Now for calculating the interest rate, we do this operation:
Interest rate = Interests for the loan / Amount of the loan
Interest rate = 40/500 = 2/25 = 0.08 * 100 = 8%
But let's remember that this is for the total duration of the loan, 3 months. For calculating the annual interest rate, we do the following operation:
Annual interest rate = Loan interest rate/3 * 12 (We use 12 because the year has 12 months)
Annual interest rate = (2/25) /3 * 12
Annual interest rate = (2/25) * 1/3 * 12 = 2/75 * 12 = 24/75 = 8/25 = 0.32 * 100 = 32%
The annual simple interest rate advertised by the bank is 32.
For calculating the effective interest rate, we will assume monthly and quarterly payments. The formula is the following:
Effective interest rate = (1+rate/payments)^payments - 1
For monthly payments (12 in a year), we replace:
Effective interest rate = (1 + 0.32/12)^12 - 1
Effective interest rate = (1 + 0.02667)^12 - 1
Effective interest rate = 1.3713 - 1
Effective interest rate = 0.3713 = 37.13%
For quarterly payments (4 in a year), we replace:
Effective interest rate = (1 + 0.32/4)^4 - 1
Effective interest rate = (1 + 0.08)^4 - 1
Effective interest rate = 1.3605 - 1
Effective interest rate = 0.3605 = 36.05%
The effective interest will be 37.13 if the payments are monthly or 36.05 if the payments are quarterly.
