A loan of size A is to be amortized by monthly payments of $1000.The rate of interest on the loan is j₁₂ = 18%.The outstanding balance immediately after the 4^th monthly payment is $12,000.How much principal is repaid in the 12^th monthly payment?

Question

Quizplus · Accepted Answer

We can use the amortization formula to find the outstanding balance after the 45th payment:

A = (PMT/i) * (1 - 1/(1+i)^n)                   [amortization formula]

where A is the outstanding balance, PMT is the monthly payment, i is the monthly interest rate, and n is the number of payments.

Plugging in the given values, we get:

12000 = (1000/1.015) * (1 - 1/1.015^45)

Solving for the monthly interest rate, we get i = 1.5%.

Now, we can find the outstanding balance after the 119th payment (i.e. after 11 more payments):

A = (1000/0.015) * (1 - 1/1.015^11) = 8922.49

Therefore, the principal repaid in the 120th payment is:

1000 - 8922.49 * 0.015 = $910.07

Hence, the answer is (C).

A Loan of Size a Is to Be Amortized by Monthly