Rebecca borrowed $20 400 from her local credit union to pay for the upgrades in her kitchen. She wants to pay the loan with monthly payments over the period of 3 years. What is the interest included in the tenth payment, if the rate charged by the credit union is 6% monthly?

Question

Quizplus · Accepted Answer

First, we need to calculate the monthly payment using the formula for the present value of an annuity:
PMT = PV*(r*(1+r)^n)/((1+r)^n - 1)
where PMT is the monthly payment, PV is the present value of the loan, r is the monthly interest rate, and n is the total number of payments.

In this case, PV = $20,400, r = 0.06/12 = 0.005, and n = 3*12 = 36. Plugging these values into the formula, we get:
PMT = $613.30

Now we can use the formula for the interest component of a loan payment:
Interest = P*(r/n)
where P is the remaining principal balance and n is the total number of payments.

For the tenth payment, there are still 26 payments remaining. Therefore, the principal balance is:
P = PV*((1+r)^n - (1+r)^(10-1))/((1+r)^n - 1) = $13,093.47

Plugging in the values for P, r, and n, we get:
Interest = $13,093.47*(0.005) = $78.19

Therefore, the answer is A) $78.19.

Rebecca Borrowed $20 400 from Her Local Credit Union to Pay