Question

You received a loan from a bank for $100,000 at an interest rate of 6%. You are expected to pay back the loan in equal monthly payments over the next 10 years.

Calculate:

1. your monthly payment

2. how much you owe after 5 years of payments

3. how much of the first payment went to interest

4. wow much of the first payment went to principal

Answer 1

1. Let the monthly payment be A. So, writing the present value equation, we have

100000 = A x (1/1.005 + 1/1.005^2 +... + 1/1.005^120) = A x 1/1.005 x (1 - 1/1.005^120)/(1 - 1/1.005)

A = 1110.205

2. The amount owed will be = 100000 - 1110.205 x (1/1.005 + 1/1.005^2 +... +1/1.005^60) = 100000 - 1110.205 x 1/1.005 x (1 - 1/1.005^60)/(1 - 1/1.005) = 42574.023

3. The first interest payment will be = 100000 x 0.005 = 500.

4. Hence, the first principle payment will be = 1110.205 - 500 = 610.205