# Amortization question

1. Jun 8, 2009

### IniquiTrance

Say I have a 5 year \$20,000 mortgage at 10% compounded annually.

To calculate the annual payment:

$$\frac{x}{(1.10)} + \frac{x}{(1.10)^{2}} + \frac{x}{(1.10)^{3}} + + \frac{x}{(1.10)^{4}} + \frac{x}{(1.10)^{5}} = 20,000$$

The first term corresponds to the first year and so on.

It would seem then that this 1st term knocks off the largest chunk of the 20k principal, since it has the largest value. Yet I know that the largest principal payment is made in the last year, when interest is lowest.

How do I resolve this contradiction?

Thanks

2. Jun 8, 2009

### CRGreathouse

Most of the first chunk goes toward interest. At least, that's how it's usually explained.