Kremena took out a
$500
discounted loan for a period of
3
months. the amount she actually received into her bank account was
$460
. assuming simple interest rates, what is effective interest rate
r
e
? give your answer as a percentage to the nearest percent. do not include the percent symbol in your 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.

2

step-by-step explanation: