Whats the third payment?

Question

You borrow $2000 from the bank at 1% annual interest compounded monthly. The monthly payment is $100. What is the balance after the third payment?

Answer 1

You begin with $2000.

After 1 month, you earn 2000(1 + .01/12) = $2001.67. If you pay at the end of the month, you then have $1901.67 left.

 

Repeating this process, at the end of two months, you have 1901.67(1 + .01/12) - 100 = $1803.25.

At the end of three months, you have 1803.25(1 + .01/12) - 100 = $1704.75 left.

 

The answers will be different if you pay at the beginning of each month. This is related to the idea of a annuity and loan amortization, but I will not elaborate on this here.