Software and Computer Engineering

The Math of Financing A House

Huge disclaimer: This is not financial advice. Do your own research and double-check the facts for the country you live in and for the specific terms you are agreeing upon.

The following is what we had to figure out to be confident we were doing a good financial decision and also to be able to draw the line between what we could and could not afford. The numbers are fictitious and for illustrative purposes.

Say you start from a condition of spending $5,000 per month on rent. This is your baseline, and any prospective housing option will be compared to that expenditure rate.

For the scenario you keep renting indefinitely, the rent does go up over time due to inflation and market forces, so you are looking at an year-over-year rent increase of, say, between 5% and 10%?

More likely than not you'd like to get out of rent and into home ownership as soon as you can, at the very least to cut on that increasing recurring cost -- unless you are planning on moving a lot for the foreseeable future.

Now you are considering buying a $1,000,000 house or apartment. If you are a first-time buyer, you most likely don't have that money upfront, so you will have to ask the bank for leverage.

Leverage is the key word here. Will have to provide with a down-payment, a substantial amount of the total investment -- say $300,000 --, only then the bank will provided the remainder. The full amount will, in turn, be immediately available for the current -- and soon to be former -- property owner, and you will have a relationship with the bank to pay the rest of the amount over time.

As you are very well aware, there's a premium for money right now instead of money later. Due to inflation and market forces, the same nominal amount right now is worth less in the future. So it means that even though you are financing “only” $700,000 right now, the bank would like a return on their investment comparable to inflation plus a premium on top, since they are so kindly supplying you the money.

Now suppose the financing terms are that the debt is to be paid in 420 months at an annual interest rate of 5%, which is roughly 0.4% per month.

For this particular arrangement, your installments are calculated as follows:

First, you'd like to make a dent on that $700,000 debt and have it paid at the end of the 420 months. So each month, the installment is at least $700,000 / 420, which is roughly $1667.

Added to that, you have to “cancel out” the debt growth due to interest. Interest is applied to the current debt amount, so it starts at 0.4% of $700,000 in the first month, then goes down over time as you pay off this total.

For the fist month you owe $2800 in interest alone, which added to $1667 we calculated before -- to pay off the total debt -- and adding in some administrative fees it rounds up to around $4500.

Well, you are already currently paying $5000 on rent and have $300,000 on hand in savings. For the financing conditions outlines above -- and assuming that you can't invest those $300,000 in a safe and guaranteed investment for which returns are likely to outpace the inevitable rent increase -- it only makes financial sense to finance a house at this value because:

In essence, you are trading: