Answer:
The annual interest rate for this loan is 16.67% or 1.38% per month.
Explanation:
Let's evaluate the information given:
Amount of the loan = US$ 1,200
Duration of the loan = 3 months
Net amount received by Billie into her bank account = US$ 1,150
Interests for the loan = Amount of the loan - Net amount received into bank account
Interests for the loan = 1,200 - 1,150
Interests for the loan = US$ 50
Now for calculating the interest rate, we do this operation:
Interest rate = Interests for the loan / Amount of the loan
Interest rate = 50/1200 = 1/24 = 0.0417 * 100 = 4.17%
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 = (1/24) /3 * 12
Annual interest rate = (1/24) * 1/3 * 12 = 1/72 * 12 = 12/72 = 1/6 = 0.1667 * 100 = 16.67% (Rounding to two decimals)
The annual interest rate advertised by the bank is 16.67% or 1.38% per month.