# Mortgage Debt Computation

### Capital and Interest Computation

Capital | Interest |
---|---|

0 | |

… | … |

- Total Interest

or

### Fixed monthly payment for a fixed rate mortgage

**c**: montly payments.**r**: montly interest rate (*since the quoted yearly percentage rate is not a compounded rate, the montly percentage rate is simple the yearly percentage rate divided by 12*.)**N**: number of monthly payment, called the loan “term”.**p**: amount borrowed, known as loan’s principal.

In the standardized calculations used in US:

**Derivation**

Amount owned this month = amount owned from the previous month + interest on this amount - fixed amount paid every month

1st term:

2nd term:

3rd term:

…

Nth term:

As at the Nth term, the payment is done, we have

or