MATH SOLVE

4 months ago

Q:
# Kremena took out a $500discounted loan for a period of 3months. The amount she actually received into her bank account was $460. Assuming simple interest rates, what is effective interest rate re? Give your answer as a percentage to the nearest percent. Do not include the percent symbol in your answer.

Accepted Solution

A:

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$ 500Duration of the loan = 3 monthsNet amount received by Billie into her bank account = US$ 460Interests for the loan = Amount of the loan - Net amount received into bank accountInterests for the loan = 500 - 460Interests for the loan = US$ 40Now for calculating the interest rate, we do this operation:Interest rate = Interests for the loan / Amount of the loanInterest 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 * 12Annual 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 - 1For monthly payments (12 in a year), we replace:Effective interest rate = (1 + 0.32/12)^12 - 1Effective interest rate = (1 + 0.02667)^12 - 1Effective interest rate = 1.3713 - 1Effective interest rate = 0.3713 = 37.13%For quarterly payments (4 in a year), we replace:Effective interest rate = (1 + 0.32/4)^4 - 1Effective interest rate = (1 + 0.08)^4 - 1Effective interest rate = 1.3605 - 1Effective 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.