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Tags: Calculator, Comparison, ANZ, CBA, NAB, St George, WestpacLender Update | 01.05.15
# Comparison Rate Definition: How is it calculated?

## LOAN TYPES

## INFORMATION

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**So what is a Comparison Rate? **A comparison rate is a tool to help consumers identify the true cost of a loan. It factors in the interest rate, fees and charges and displays a single percentage rate that can be used to compare various loans from different lenders. From 1 July 2003, the Australian Government made it mandatory to display a comparison rate for any advertisement of a credit rate - including home loans.

**Factors effecting Comparison Rates?**

Comparison rates are calculated on a number of factors, including:

- loan amount
- term of the loan
- repayment frequency
- interest rate
- fees and charges (excluding government charges, such as stamp duty and mortgage registration fees)

**How is the Comparison Rate Calculated? (with example)**

The comparison rate is calculated based on the following numbers, no matter what your loan size is:

- $150,000 loan amount
- 25 year term
- principal and interest loan

As shown above, the loan amount is actually based on $150,000, which is much smaller than the average home loan size in Australia (at the time of writing the average is $365,000). This means that any home loan that has fees associated with it, those fees have a larger than expected impact on the comparison rate.

For example, let's look at NAB's professional package: NAB Choice Package Home Loan. The example would be similar for CBA's Wealth Package, St George's Advantage Package, Westpac's Premier Advantage Package and ANZ's Breakfree Package.

- NAB Choice Package home loan details:
- Interest rate: 6.97% p.a. (please note: this rate is accurate at time of writing in 2011)
- Establishment fee: $0
- Monthly fee: $0
- Annual fee: $395

Because of the way the comparison rate is calculated, the comparison rate for this product is 7.31% p.a. Let's have a look below at two examples, one with a loan size of $150,000 and another with a loan size of $500,000 so you can see how the proportion of fees effects the cost of your home loan.

**$150,000 loan size**

- Term: 25 years
- $167,190 in interest over 25 years
- $9,875 in fees over 25 years
**$177,065**in total over 25 years (excluding principal component)**5.6% of cost is made up in fees ($9,875 / $177,065)**

**$150,000 at 7.31209% interest over 25 years with $0 fees gives you exactly $177,065 in interest.****7.31209% rounded to 2 decimal places is 7.31%****= 7.31% comparison rate**

**$500,000 loan size**

- Term: 30 years
- $693,920 in interest over 30 years
- $11,850 in fees over 30 years
- $705,770 in total cost over 30 years (excluding principal component)
**1.7% of cost is made up in fees ($11,850 / $705,770)**

**$1,500,000 loan size **(to highlight the difference)

- Term: 30 years
- $2,081,760 in interest over 30 years
- $11,850 in fees over 30 years
- $2,093,610 in total cost over 30 years (excluding principal component)
**0.6% of cost is made up in fees ($11,850 / $2,093,610)**

With the difference of 1.7% (or 0.6%) in fees to 5.6% in fees, you can see that the comparison rate is being dramatically affected at the lower loan amount and depending on your loan size the comparison rate may not actually be a good comparison tool for your situation... Try to keep this in mind when comparing home loans.

Back « St George Advantage Package ReviewThank you for your feedback. Is there anything in particular we can provide to assist you? Please let us know and we'll do our best to add to the article. Thanks

like the first guy has said, it does not actually show HOW comparison rate is calculated. maybe you can put it in? like the formula and how to use it, what can it do and such. thanks

Well the question remains.... "Comparison Rate Definition: How is it calculated? " Like to give EXACT figures and values on how you calculated it? - or were you hoping we simply take your word for it, that whatever method you used it's correct? ;)

Thanks for your question Paul.

Unfortunately, there is no simple formula for comparison rate, but I can show you a simple example step by step:

Sample loan: - 6.50% variable - $350 per year fees

1) The government has mandated that all comparison rates are calculated on $150,000 over 25 years, so you use these numbers.

2) Use the compound interest formula to work out exactly how much interest on $150,000 over 25 years on a principal and interest loan is $153,843. - Reference compound interest formula (be sure to factor in principal and interest payments): http://en.wikipedia.org/wiki/Compound_interest#Compound

3) Add yearly fees of $350 x 25 = $8,750.

4) Total interest and fees is $162,593.

5) Now we need to work out what the actual interest rate needs to be to get $162,593 in interest over 25 years. Use the compound interest formula again to find what percentage is needed to get $162,593 in interest as the answer.

6) For this example, the comparison rate is 6.81%.

We welcome your feedback.

Dear Sir or Madam

Your first calculation seems to be incorrect; $150,000 loan size •Term: 25 years •$167,190 in interest over 25 years •$9,875 in fees over 25 years •$177,065 in total over 25 years (excluding principal component) •5.6% of cost is made up in fees ($9,875 / $167,190)

I think you should divide $9,875/$177,065, not by $167,190.

Cheers Matt

Thanks for your feedback Matt. You are absolutely correct. That was a typo on our part and is now updated.

I see some car retailers quoting 1.5% comparison rate for 5 year term.Please explain how this comes about when the interest rate is much higher JIM

So when car yards are offering 1% comparison loan on a car what are meaning

You guys keep asking stupid questions about how, how, how... Why don't you: Step 1: read Step 2: think

If most people realized that they're actually paying back more than double the amount of money they originally borrowed over the life of the loan. Wonder how many people would consider buying beyond their means. Instead of focusing on stupid things like comparison rates, shopping around. Why not just borrow less and live in a more affordable home/area. Keeping up with the Jones and wanting more than you can afford is the real problem here!

Barry and Paul are correct. For all the average folks out there that are not great with math towards interest, Please show all workings to find out comparison rate. Saying to use the compound interest formula is no help to most people. How is it worked out.

It means that the loan interest and fees added together are equal to a total interest rate of 1%

Car retailers are quoting 1.5% comparison rate. The finance manager told me the deposit is 20% of the purchase price of the car. The rest is the amount to borrow. The finance manager now told me the 1.5% comparsion rate is not included the establishment fee and charges, the monthly repayment is in fact based on the amount to borrow that is (80% of the purchase price plus extra $780 establishment fees). I am shocked that the establishment fee have never been mentioned before and now it is an add on. I am very upset about the way they advertise the low rate and not mentioned the extra establishement fee to client until you ask.

comparison rate is just garbage. tell me what reducible interest rate i am paying on a loan when it includes ALL fees and charges rather than a figure that actually means nothing.

Great explanations. I now have a good understanding of what a comparison rate is. Thanks. Oh Jeff, pull your head in champ.

Oh what a lovely world we live in

Comparison rate???, what a joke... It seems that the finance sector has taken a leaf from Ms Gillards book, ie lie, confuse, and hide the true figures by giving them new names, but ripp em off harder than ever before. Seems the educated ones" think the rest of us "intelligent" ones are all stupid???? One simple question, Why can't they just be honest?

Despite all the gooblydegook, I am still none the wiser. What is the 'compound interest rate formula'. Exactly (show figures) how do you work out $177,065 interest on a loan of $150,000?

Woulden't it be nice if you would set out a simple example of borrowing, say $20,000 on a car. Show all details including price of car, deposit required, establishment fee, GST, charges, interest etc. Try to imagine you are explaining to your 8 year old son!

I'm confused by comparison rates when looking at home loans. I have found that some banks have a lower interest rates and lower annual fees but the comparsion rate is still higher than one with a higher initial interest rate and higher annual fees so I'm wondering how that can possibly be right? It would help if you could show two examples with the same amount being borrowed (i.e. $200,000) but with different interest rates and annual fees and show how the comparsion rates work - particularly focusing on any hidden costs which may alter the comparison rate. I hope that makes sense.

Thank you for the explanation.From this summation to get an accurate comparison rate for the amount you are borrowing the following calculation is required......

1.Divide your borrowing amount by 150,000

2.Subtract the interest rate from the comparison rate.

3.divide the answer to step 2. by the answer to step 1.

4.now add the answer to step 3. to the interest rate.

You will then have a more accurate comparison rate tailored to the amount you are borrowing. I hope this helps you readers.

People are commenting a lot about hidden costs such as Lori. Keep in mind that is the whole reason the govt came up with the comparison rate.So people better understand there total costs.These must be disclosed by LAW.

Another perfect example of our need to be ever vigilant. Corporate Australia views we consumers as idiots, treats us with disdain, lies to us every chance they get and plants the onus firmly on our shoulders to catch them at it and then fudges with more lies in a vain attempt at excusing their deliberate deceptive practices. Professionalism does not exist in this morally bankrupt country.

I still do not understand this bloody comparison rate . The banker offered me $310000 for the intrest rate 5.19 percent but the said this is not the end of the story I have to pay more bcos of the comparison rate

Too many people are reading the incorrect assumption into the caparison rate. It is a straight forward formula used by all banks and building societies.

Forget the interest rate amount and compare lenders by the final figure of the comparison rate that is the one that count.

Match apples with apples so to speak to get the actual rate to be charged and then hunt for the best comparison rate.

"With the difference of 1.7% (or 0.6%) in fees to 5.6% in fees, you can see that the comparison rate is being dramatically effected at the lower loan amount..." Please learn the different between effect and affect.

It is plain and clear like a daylight that nobody here (including myself, including this Tomorrow Finance) knows about how to actually calculate Comparison rate. There is not a single clear example of the real calculation. Examples given here by all to find the comparison rate already includes "comparison rate" before hand. Most of us wants equation for comparison rate.

Paul, with all due respect, in your instructions above, where do you actually get the "comparison rate" in your step 2.

Thank you ZDM. The spelling error has been corrected.

Denis, As I understand from the article the comparison of "apples with apples" has decreasing relevance as one moves further above a loan amount of $150,000. Ie. typically the interest rate becomes more important and the fees less so as the loan amount increases.

so does this mean, I borrow (for round figures) $30 000 for a car. so all loans are calculated at $150 000 for comparison. so if comparison rate is 1%, the rate I am really paying is 5 times that? eg 150/5 = 30. so rate is 5%?? This is confusing..

So does it mean that when we look for home load, it is more important to compare the comparison rate between lender, than the home loan rate?

Sorry, should be home loan, not home load.

The comparison rate is a joke. We borrowed $10,000 towards a car at a comparison rate of 2.5% over 3 years and asked if there was any sort of establishment fee - guess what the answer from the dealer finance lady was NO. We were only borrowing it to get the 3 "free" services - we had weighted up the cost of the services compared to the interest payable over the life of the loan and the financing was the way to go. BUT (and there is always a BUT) and I mean but when we were signing up, suddenly there was a $495 establishment fee they thought they could slip in without us knowing - very deceptive (under section 52 of the trade practices act - deception). So we told them to shove the loan and just paid for the car - to never deal with that dealership again. The moral to this story is research, read and think about ones actions!

Advertising by car dealerships is made to confuse. By advertising a 1% comparison rate the poor unsuspecting buyer thinks they are getting a great deal. Very few buyers are savvy enough to do the calculations and realise what is really going on.

Thank you Finance Tomorrow. All makes sense. Despite some of the responses, there are those of us who actually do understand what you've explained.

so am i correct in guessing that the comparison rate will never be less than the actual interest rate? ie if i want to buy a car for 25000 at a .5% comparison rate, does this mean that the actual interest rate should be lower because the fees r also included in the comparison rate?

Look back through the thread, you will see that a link was provided for the compond interest rate formula. Read and think is good advise with less spoon feeding

You will always pay the interest rate plus what ever fees and charges that the lending institution adds on. The Government instructed all lenders or finance providers to combine these two factors ie interest rate plus charges to arrive at a comparioson rate (see meaning of the word comparison) In this way you as a consumer can see that whatever the advertising and sales pitch is you can Compare, (that word again) real charges that are applied to that finance between one lender and another. Unfortunately some advertising is misleading when they say 1% comparison rate so as always "Caveat emptor". The governments intent was genuine although application very confusing. If you are unsure about any loan document take it to an indepedant CPA before signing.

Is there a simpler formula to understand comparison rate

Not sure how you managed to get •$167,190 in interest over 25 years
for the example of 150k loan? I used the compound interest formula
=P*(1+(r/n))^(n*t). Working this out gives me $574,154 in interest alone over the life of the loan. Correct me if I am wrong on this

comparison rate means nothing. advertiser should show the actual rate and total amount to pay back that way people know exactly what they are up for! comparison rate is just another thing to help sell products and sucker people into paying more then they expect

Alternatively. You can ask any potential lender to add all interest, fees and charges into the term of the loan and give you an Armotised monthly payment figure for a fixed term. Whoever has the lowest repayment figure will be the cheapest alternative. Armotised figures dont lie and dont need any other understanding other than the lowest repayment amount is the lowest overall cost of that particular loan.

"5) Now we need to work out what the actual interest rate needs to be to get $162,593 in interest over 25 years. Use the compound interest formula again to find what percentage is needed to get $162,593 in interest as the answer.:

Actually, to calculate the comparison rate it isn't a simple case of using the compound formula.

Comparison rate mathematics is very complex as you have two unknowns. The majority of the calculators on the net are not very accurate either. If you put their Comparison Rate in a simple loan calculator, and the loan amount used you can compare the results and see the totals are quite different. Bizz Tools have a very accurate one but ANZ's calculator is about .25% off which gives a huge difference on large loan amounts. Even Cannex's calculator is out by a significant amount.

Nice one Maths Man - you got it totally wrong! Interest on a $150k loan @ 6.97% over 25 years. Based on a principal and interest repayment plan does equate to $167,190 in Interest value.

Is it hard to simple give the maths formula of comparision rate calculations? as I am not able to achive 7.31% comparison rate for the first example I user the formula to compute interest but I gives a lower number than 7.31

I think the formula http://en.wikipedia.org/wiki/Compound_interest#Compound will not work as home loans deduct interest on a reducing amount * rate basis, so the formula we have gives us effective rate and not comparision rate. please provide steps/ formula so it is more clear.

Please show the formula you used with figures plugged in for the above example •Term: 25 years •$167,190 in interest over 25 years •$9,875 in fees over 25 years •$177,065 in total over 25 years (excluding principal component) •5.6% of cost is made up in fees ($9,875 / $177,065)

I've tried the formulae from wiki... and always get larger results. Thanks and regards

Some of you gents and ladies need to go back to high school and learn some maths

You all realise that this formula and calculation is all academic right? Yes, it is used to highlight the cost of credit so that you don't focus on the rate alone but include fees and charges (AND rate changes where you have a fixed rate reverting to a variable rate), however the variabillity of any variable rate loan will mess with the ACTUAL cost! Not to mention that the Wiki formula is a generic formula and may not be used by each bank. Each bank will have it's own system that calculates depending on a specific formula and will take into account rounding ona daily basis. (Of course the forumals will be signed off by an actuary and be legaly compliant, but may produce favorable results in soume cases due to the rounding factor.) To throw a spanner in the works this is all dependant on when you PAY each repayment! If you have the abillity to make advance repayments at no penalty on a loan(and can do so) then the comparison rate is meaningless when you compare the product with an alternitive that does not give you this feature.

Yes comp rates are very important, but consumers need to take into account a whole multitude of factors and not try to rely on a simplistic explanation.

Being new to Australia I asked my fellow work mates about comparison rates and they had no idea what it is all about. People are still borrowing blindly, especially cars.

The 1% figures quoted are meant t OK attract the poor Joeys into debt.

To calculate the actual interest paid over 25 years, one needs a calculator that calculates loan amortisation not just simple fixed interest.

The mathematics involved is complex and not useful to any ordinary consumer.

For goodness sake, why is the comparison rate based on $150K over 25yrs? There is no house on the market that cost that little.

Comparison Rate Formula

The calculations to find Payment are based on an annuity formula in common use.

For convenience the frequency at which the fees and charges are paid is assume to occur on the same day date as each and every instalment during the currency of the loan.

That being the assumption in the above case 9,875.00 assumed to be paid during the currency of the loan divided by 300 [25 years] = 32.91 per month. This is the notional addition payment covering fees that is required to be paid during the currency of the loan that has to be expressed as an interest rate rate.

Monthly coincidental Instalment and Interest Rests with Payments in Arrears. First Instalment is assumed to occur one interval after the fund date and then on the same day date in every month or the last day of that month which does not have that day date [29, 30 and/or 31].

150,000 6.97% 300 Months [25 Years] Monthly Payment 1,057.30 Total Interest 167.190.00

Amortised Fees [25 years Total 9,875 / 300 number monthly payments) = 32.91 per month.

150,000 7.31% 300 Months [25 Years] Monthly Payment 1,090.21 [1,057.30 + 32.91] Fees = 9,875 Interest = 167.190 Total Equals 177,065.

Proof (300 @ 1090.21) - 150,000 = 177,063

The difference 2.00 is due to rounding in the formula.

Different results using the same amount of loan for Fortnightly or Weekly intervals will produce a different Comparison Rate.

Well....I'm freakin confused!!! But also a little more cautious of the banks sneaky tactics designed to confuse and deceive 'average' citizens without 'advanced' math skills.

Hi Mate u can calculate on Excel by using "PMT formula" Step 1:

Monthly Payment in normal rate @6.97% =-PMT(Rate,nper,pv) = $ 1057.30

ie, Rate= 6.97% / 12 (12 for months, 26 for weeks, 52 for fortnights) nper= 300 (months) pv = 150000

Total Payback with interest= $ 1057.30 X 300 months = $ 317,190.00 Total Interest = $ 317,190 - $ 150,000 = $ 167190

Like everything specified by Treasury, comparison rates are over-complicated mandatory gibberish which few people understand or use.

To illustrate my point, here is the legislated way to calculate a comparison rate on a small amount credit contract :

Calculation of comparison rates

```
(1) For section 166 of the Code, comparison rates are to be calculated in accordance with this regulation.
(2) The comparison rate must be calculated as a nominal rate per annum, together with the compounding frequency.
(3) The comparison rate is calculated using the formula:
where:
```

n is the number of repayments per annum to be made under the credit contract (annualised if the term of the contract is less than 12 months), except that:

```
(a) if repayments are to be made weekly, n is 52.18; and
(b) if repayments are to be made fortnightly, n is 26.09; and
(c) if the contract does not provide for a constant interval between repayments, n is to be derived from the interval selected for the purposes of the definition of j .
```

r is the solution of the following:

```
where:
```

Aj is the amount of credit to be provided under the contract at time j (the value of j for the provision of the first amount of credit is taken to be zero).

"Cj is the fee or charge (if any) payable by the debtor at time j in addition to the repayments Rj" , being a credit fee or charge (other than a government fee, charge or duty) that is ascertainable when the comparison rate is disclosed (whether or not the credit fee or charge is payable if the credit is not provided).

"j" is the time, measured as a multiple (not necessarily integral) of the interval between contractual repayments that will have elapsed since the first amount of credit is provided under the credit contract, except that if the contract does not provide for a constant interval between repayments an interval of any kind is to be selected by the credit provider as the unit of time.

"Rj is the repayment to be made at time j" .

"t" is the time, measured as a multiple of the interval between contractual repayments (or other interval so selected) that will elapse between the time when the first amount of credit is provided and the time when the last repayment is to be made under the contract.

```
(4) The comparison rate must be correct to at least the nearest one hundredth of 1% per annum.
(5) In the application of the formulae, reasonable approximations may be made if it would be impractical or unreasonably onerous to make a precise calculation.
```

Example: If repayments are to be made on a fixed day each month, it may be assumed that repayments will be made on that day each month even though the credit contract provides for payment on the preceding or succeeding business day when the due date is not a business day.

```
(6) The tolerances and assumptions under sections 180 to 182 of the Code apply to the calculation of the comparison rate.
(7) The comparison rate must be accompanied by a statement of the amount of credit on which it is based and the term for which credit is provided.
```

It won't even print the formula because the word processor on this page does not recognise the fonts !! Enough said. Gibberish.

Had an hour conversation with the bank via online chat, they could not answer what comparison rate actually is as well as here. However, this page still isn't clear.

My understanding is a comparison rate is ABOVE the standard variable rate by the amount of fees to be added to the loan at an amount equal to a borrowing of exactly 150K. Comparison rate is a trick because if you borrow 300K your fees don't double, but the comparison rate interest is payable as if the fees did.

Because most borrowers are chasing a good interest rate, credit providers simply need to increase fees, and provide lower interest rates to attract lenders. Because fees are so high, the banks will lend you money for their fees.

Instead of adding the actual dollar amount of the fees (calculated as all expected fees for the 25 year term of the loan) to your principal amount at the beginning of the loan. The banks are waiving these fees in a way and increasing the interest rate to the higher comparison rate to cover the costs of the bank fees as higher interest amounts over the term of the loan.

So now banks can claim interest not only on the principal borrowed, but can increase the standard variable rate % amount by adding all expected fees at the start of the loan and increase the overall interest rate of the loan.

if the comparison rate is 0.5% higher than the standard variable rate, on a 150K loan you will pay an extra $9554 in interest over 25 years ($102 per year)

On a 500K loan an extra $31,846 over 25 years ($1274 per year)

The biggest print on car ads is comparison rate, where tears ago it would how much a week it was going to cost. Really the bottom line is always the important thing whether you understand comparison rate mumbo jumbo or not

should read years not tears

So are you saying that having the lowest comparison rate might not provide you with the cheapest loan?

Hi, All readers please note: This article heading is: "Comparison Rate Definition: How is it calculated? meaning that when you read it you are expecting to find out how this calculation is done, But isn't this funny when you reach the point the writer says: """Because of the way the comparison rate is calculated, the comparison rate for this product is 7.31% p.a.""

So you conclude that either the writer does not know it either and what is being written is a load of abalone. Or he/she is biased and does wants to get you!!!

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barry21/05/2011this eg does not give enough detail showing how the calulations are made

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