Question

Kremena took out a

Answer 1

Answer:

The correct answer is 32%.

Answer 2

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.