# Are you paying more interest on your mortgage than you think?

The way banks calculate interest means that mortgage holders may be paying more than they expected, write UNSW Business School’s Kevin Li and Sander De Groote

If you're a homeowner, you’ve probably been on edge for the past few months. To keep up with the incredible boom in housing prices, many Australians took advantage of the low-interest rates, and increased their borrowings. Since over 10 years ago in December 2012, the cash rate has been 3.0 per cent or lower, with rates dipping below 1.0 per cent in October 2019, before dropping all the way to 0.10 in November 2020, during the covid pandemic.

But now that inflation is rising, the RBA has been pulling up the cash rates since May 2022, despite its initial forecast that it would not do so until 2024. And in the process of this fight against inflation, some homeowners are heading for trouble. For every 0.5 percentage point increase in the cash rate that is fully passed on by the banks, a borrower with a $737,478 loan (the average NSW loan as of October 2022, according to the ABS), will pay about $230 amount more monthly. a Roy Morgan released in November 2022, 1.013 million mortgage holders (22.6 per cent) were ‘at risk’ of ‘mortgage stress’ in the three months to October 2022.

These are the kind of figures that make one want to go feverishly over your own loan calculations in detail – which is exactly what we did when it came to our own home loans. But when we did the sums, we discovered a glaring issue, that we previously had not noticed when we signed the contract. Our mortgage interest charge is calculated using a method that could cost us over $10,000 more than we thought initially over a loan’s lifetime.

## How interest charges are calculated

First, we need to take a step back and explain some banking (and maths) basics. There are two ways of calculating your interest charges – simple and compounding interest (check out our explainer box to see what the difference is). The simple interest rate method divides an annual rate by the number of days in the year to get to a daily charge.

In contrast, compound interest uses more complicated calculations that consider when interest is charged to a mortgage.

Common logic tells us compounding interest is more expensive for home loan holders. But in fact, this is not always the case. For the same level of annual interest rate, the simple interest method will lead to a higher daily interest rate than the compound interest method.

Read more: What happens to the economy if people can't pay their home loans?

When converting your annual mortgage rate (which is communicated in percentages) to a daily rate, simple interest always gives a higher daily rate compared with the compounding interest method. Result? The interest charged is higher than what you would think it is based on the interest rate in your contract.

Simple interest uses, as its name suggests, as simple calculation. When converting an annual interest rate to a daily rate, the annual rate is divided by 365. For example, if you want to allocate a 6 per cent annual rate to 12 months the formula works as follows: (1+0.06)/12-1=0.005.

Compound interest takes the frequency of interest charges into account when converting an annual rate into a daily rate. Specifically, to correctly calculate the interest for n equal periods in a year, the n^{th} root of 1 + the annual interest rate is taken and the 1 is subtracted again to correctly allocate the charges. For example, if you want to allocate a 6 per cent annual rate for 12 months the formula works as follows: (1+0.06)^{1/12}-1=0.00487.

## Simplifying complex interest calculations

The issue with the above is that it is quite complicated to understand for the average person looking to take out a home loan.

Here is it spelled out with an example. When you are shopping for a mortgage, you are quoted annual interest rates in an offer. This rate is then made official in the mortgage contract when you sign, and is almost always expressed on a yearly basis in the contract. But after actually taking out the mortgage, the actual interest charge is not usually on a yearly basis. For most mortgages it is monthly, and the annual interest rate is converted using simple interest rate calculations to charge the interest each day.

Say you take out a loan for $100,000 and pay back the whole amount in one year with an annual interest rate of 5 per cent. For a loan like this, you would expect to pay back $105,000 by the end of the year.

So far so good? The next part is where the problem lies (and why this loan might end up with a $105,116 balance instead).

Read more: How credit supply and loans to investors impact housing prices

Now, instead of one $5000 charge at the end of the year, your loan gets interest charged to it monthly. This way which uses the simple method makes it very similar to how most mortgages work and is one of the reasons why they end up more expensive than you would think.

We’ve broken down how this works:

- The interest rate in your contract is divided it by 365 – the number of days in a regular year. This gives you a daily interest rate.
- Then this smaller daily rate is multiplied by the outstanding balance of your loan each day of a month – say, 30 days. This results in a daily amount of interest.
- Once a month, interest is charged to the mortgage. This monthly charge is the sum of all these daily interest amounts calculated over the last month.

This is the problem. At the end of the year, if we use this system the amount you need to repay on your $100,000 loan will not be $105,000, as you initially thought. In fact, it will be $105,116.

This is because the simple interest method only gets you to $105,000 if no interest charges are made until the year's end. By adding interest to your balance at the end of each month, you end up being charged a little bit more interest the next month. This is because, in each day of the next month, we multiply the daily rate with a slightly higher loan balance. The end result of this is that the final annual interest on this loan is higher than what the customer might have thought was suggested in the beginning.

If instead of using simple interest, we use compound interest to calculate the interest rate charges for this loan it does not matter over which period we add interest. At the end of the year, the final balance will always be $105,000.

Why is this? Because when interest is added using the compounding interest method, the increasing balance over the year is considered in the calculations. By taking into account the interest period, the charge is adjusted so that the end result is always the correct annual interest charge.

Read more: Australia's mortgage interest rates are fixed for shareholders, not home owners

## Applying the calculation in practice

In July 2023, the average size of a new mortgage in NSW was about $750,000. The average interest rate for these new loans was about 5.95 per cent.

Using the simple method described above, the monthly payment for this mortgage is $4473. This is also the amount you will find on most mortgage calculators. If instead, we use compound interest the monthly payment goes down to $4398. This is a $900-a-year difference – savings that add up over the decades of repaying the loan.

For example, over the whole 30-year lifetime of the loan, that difference alone adds up to a total of almost $27,000 – nothing to be sneezed at. In the end, this all means that the interest you are effectively paying on your mortgage is higher than you might have thought.

## Banks and interest rate calculations

Between us, we have checked the terms and conditions of the big 4 banks (Westpac, CommBank, ANZ and NAB) and their biggest subsidiaries (St. George and Bankwest). They all charge interest using simple interest calculations. Mutual banks – a bank that is owned by its customers – have different reporting requirements, but those where we could find the interest calculation method, also apply the same technique as the commercial banks.

In general, the terms and conditions that came with your mortgage will include a paragraph that explains the way interest is charged. This is usually somewhere in the middle of the document, and often includes a formula and a paragraph of explanation. The rub is that while this information is hard to find, it is not impossible. Dive deep into the terms and conditions of your mortgage and you will find this calculation among the stack of paper, eventually.

Alternatively, customers can call the service line, ask specifically about the formula and work out the calculations themselves. This is what we did, but we feel this puts an unnecessary burden on customers to understand all this complicated maths.

Sure, it is technically disclosed very deep in the document, with complex algebraic formulas – but what average Australian home buyer reads the disclosure or has that level of mathematical understanding?

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## Read the terms and conditions

The way that we can begin to resolve this as a community lies in both raising financial literacy, and awareness of how home loans work. Banks, however, can make this process a lot easier. Rather than quoting interest rates only on an annual basis, a clear rate that covers the same time period as the interest charge period should be communicated.

On an individual level: read the terms and conditions carefully, including the formulas. This is one of the biggest financial decisions you'll ever make. If in any doubt, it’s worth getting a financial counsellor involved to review the contract.

*Dr Sander De Groote** is a Lecturer and **Dr Kevin Li** is a Senior Lecturer in the School of Accounting, Auditing and Taxation at UNSW Business School.*

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