# How is mortgage interest calculated?

Home loans can seem complex and intimidating. This may be partly due to the massive sums of money involved, especially for buying property in Australia’s capital cities. It may also be partly due to the seemingly impenetrable maths involved in working out your interest charges and monthly repayments.

Your high school maths teachers may have included simple interest and compound interest formulas in their curriculums, and even loan interest and repayment formulas. But if your memories of those days are fogged by time and a cloud of hormones, here’s a quick refresher on how mortgage interest and repayments are calculated, so you can make your very own “back of the envelope” home loan estimates.

Please note – RateCity isn’t a maths teacher, and should not be relied upon as a source for students. Check with your teachers, read your textbooks, and always show your working.

Also, individual banks and mortgage lenders may use slightly different calculations to work out their interest charges. Always check with a lender how they calculate your mortgage before signing on any dotted lines.

## How to calculate mortgage interest

Many banks and other mortgage lenders calculate your interest daily, and charge you monthly, when you make your scheduled home loan repayment.

You can find the interest charged on your home loan each day by using this formula:

P x (r ÷ n) = A

• A = amount of money – in this case, the daily interest charge
• P = principal – the loan amount still owing on your mortgage
• R = rate of interest – keep in mind that for use in these calculations, your advertised interest rate percentage will need to be divided by 100, hence the name “percent” which is Latin for “out of 100”.
• N = amount of time – Because interest rates are “per annum” or yearly (Latin again), this figure should be how many of the time unit you’re looking for takes place in one year e.g. 12 months, 26 fortnights, 52 weeks etc.

For an example, if you had a \$500,000 mortgage and were paying interest at a rate of 3% per annum, here’s how you could work out your initial daily interest charge:

\$500,000 x (0.03 ÷ 365) = \$41.10

Assuming you’re in a month with 30 days, this would mean that your lender will charge you around \$1233 in interest on your \$500,000 in the first month.

Keep in mind that as you lower your mortgage principal by making mortgage repayments each month, the daily interest you’re charged will change.

## How to calculate your home loan repayments

To find how much a lender will likely charge you per month for a home loan, including principal and interest, you can use a slightly more complex variation of the previous formula:

P x (r ÷ n) x (1+(r ÷ n)n ÷ ((1+(r ÷ n))n -1)) = A

I promise, it’s simpler than it looks.

So, using the previous example of a \$500,000 loan to be repaid in monthly instalments at an annual interest rate of 3 per cent over a term of 30 years (that’s 360 monthly repayments), here’s what this would look like:

\$500,000 x (0.0025 x (1.0025)360 ÷ ((1.0025)360 -1)) = A

Whipping out a calculator to handle some of the operations (though you COULD multiply the brackets by themselves 360 times…), we get…

\$500,000 x (0.0025 x 2.4568422115 ÷ 1.4568422115) = A

Which gives us…

\$500,000 x 0.004216040337289 = \$2108.02

This means that by paying around \$2108 per month for 30 years, you’ll be able to gradually pay off not only your home loan, but the lender’s interest charges.

While more than half of your initial monthly repayment will be made up of interest charges (\$1233 out of \$2108, according to our previous calculations), this will change over time, as each repayment shrinks your mortgage principal, little by little.

If you make extra repayments onto your mortgage, such as when you get a tax refund, or your variable interest rate falls but you keep making the same higher repayments, they will go directly onto reducing your mortgage principal. The faster you can shrink your principal, the more you can lower your interest charges, potentially saving you more money and helping you pay off your property sooner.

## Using a mortgage calculator

Does this all sound too hard? Would you prefer to press a button and have all of this worked out for you? Sounds like you could use a mortgage calculator

These online tools are available from comparison websites like RateCity, as well as from banks and mortgage lenders. All you need to do is enter a few details to get the results, which you can even view as a spreadsheet of repayments, with principal and interest amounts laid out month by month for full loan term. There are a wide variety of different calculators available for solving different personal finance problems.

Keep in mind that mortgage calculators (and the formulas above) rely on certain assumptions, meaning the results should be considered estimates only, and may not match up exactly with what you’d pay in real life. For example:

• Assuming you’ll be paying the same interest rate for a full 30-year loan term, which is unlikely if you have a variable interest rate.
• Assuming that every year and every month have the same number of days, when we all know that doesn’t match our calendars.
• Only being accurate for the values entered into the calculator, and not including fees and extra charges, or the effect of extra repayments, offset and redraw on your mortgage.
• Different lenders may calculate their home loans differently, such as rounding up some numbers or rounding down others, which could affect exactly how much you’ll pay.

Talking to a mortgage broker could be a good way to prepare your mortgage calculations before thinking seriously about a home loan. These home loan experts can crunch the numbers on your behalf, and answer any questions around exactly how certain home loan features and benefits could affect what you pay. And once you’re satisfied with the numbers involved, a broker can help walk you through the mortgage application process, saving you time and hassle.