Question

Billie took out a $1,200 discounted loan for a period of 3 months. The amount she actually received into her bank account was $1,150 . What is the (simple) interest rate for this loan? Give your answer as a percentage to the nearest percent.

Answer 1

The answer is 17%

Answer 2

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.