So... you got a mortgage?

Intro

This is my attempt to help visualize the impact of variable changes when selecting a mortgage.

The three variables we'll use for now are: loan amount, years and interest rate.

Here is the math I am using to compute the monthly payment:

where $r$ is the interest rate, $P$ is the loan amount and $N$ the number of years.

Cumulative amount paid in interests over time

Let's start by plotting the cumulative amount of money paid against the interest for an amount of one million dollars over thirty years with different interest rates.

The first we notice is we are paying a lot of money towards the interests instead of the principal on the first years. And that is independent of the interest rate. The value of the interest rate gets more relevant at the end of the life of the mortgage, particularly in a thirty years mortgage. This suggest making extra payments towards the principal is important.

Making extra payments

Let's explore that. Same variables but sending different amount every month:

We can see here that extra payments towards the principal have a significant impact in the amount of money we pay in interests. A couple of extra payments a year leads to 234k in savings, reducing the mortgage by twelve years.

Another interesting thing to notice: you are going to pay a lot of money in interests in the first part of the mortgage. The monthly payment equation they use (1) sends most of the payment funds towards the interests and not the principal during the first part of the mortgage.

Exploratory tool