# Mortgages

Many of you will be taking out a mortgage one day. There are several facets to a mortgage, which makes it a little more complicated than many other loans. For example, you can choose to go with a floating interest rate (danger! E.g. the ARM -- Adjustable Rate Mortgage -- mortgages that have played a role in the Sub-prime lending crisis). Let's consider only the Fixed Rate Mortgage.

We bought our house in 2001, for $120,000. We decided that we would put$50,000 in as a down-payment, meaning that we would need a mortgage for \$70,000. My own mortgage is a 15-year mortgage, meaning that we will pay off our loan in those 15 years. We got an interest rate of 5.25%, which is compounded monthly (so that's not an APR, which would be approximately 5.38% in this case).

Mortgages are often designed so that we pay a fixed amount every month: how much will we be expected to pay each month?

This can be obtained using the formula

${\displaystyle c={\frac {r}{1-(1+r)^{-N}}}P}$
where
c is the monthly payment;
N is the number of monthly payments;
r is the monthly interest rate, expressed as a decimal; and
P is the principal of the loan.

The derivation of this formula is carried out at this website.

Here's an Excel spreadsheet illustrating the calculation, and also some built-in functionality that Excel has for doing financial calculations like these (the PMT function).