How Much Can You Borrow?

Works backwards from the payment you can afford to the loan it supports. It is the fixed-instalment formula solved for the principal.

Explanation

Instead of asking what a loan costs each month, this asks the reverse: given what you can pay each month, how much can you borrow?

P = M \times \dfrac{1 - (1 + i)^{-n}}{i}

Here $M$ is the affordable monthly payment, $i$ the monthly rate and $n$ the number of payments.

Example

You can afford 100,000 a month, over 35 years, at 1.5% a year.

Loan supported — 32,660,000
Total paid — 42,000,000
Interest — 9,340,000

What interest rates really do

Hold the payment at 100,000 a month for 35 years and change only the rate.

0.5% — you can borrow 38,520,000
1.5% — 32,660,000
3.0% — 25,980,000

Going from 1.5% to 3% is a change of "only" 1.5 percentage points, and it wipes out nearly 7 million of buying power without your monthly payment moving at all.

This is why house prices and interest rates move against one another. When rates rise, the same buyers can bid less, whatever the asking price says.

Watch out

A bank does not lend on this number alone. It also caps the debt-to-income ratio, typically insisting that total annual repayments stay under 25 to 35% of your income.

And affording the payment is not the same as affording the house. Property tax, insurance, maintenance and management fees continue for as long as you own it.