Compound interest, AER and APR explained
Interest rates indicate the price at which you can borrow money. It can get seriously complicated, with many anomalies, so for starters this guide covers the basics first.
If you want to know all there is to know, including the difference between APR and AER, then step it up a notch and read to the end. If it gets too much, just stop – understanding the basics alone is the most important bit!
In this guide
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The interest rate you pay to borrow
If you borrow money and the interest rate is 5% a year, it will cost you 5% of the amount borrowed to do so. This will need to be repaid along with the original money you borrowed. Interest rates are usually quoted annually, but not always, so make sure you check.
An example to clarify
How much does it cost to borrow £1,000 at 10% then repay it six months later?
Let's start with a simple sum. One year at 10% would cost you £100 (10% of £1,000). So over six months you'd pay about half that, ie, £50. It really is almost as simple as that.
The reason I say 'almost' is it isn't exactly half of that, due to compound interest (see below). However, this is a good rule-of-thumb way to think about it.
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The interest rate when saving or in credit
This works in exactly the same way, and there's a simple reason why. When you are in credit or saving with a bank, you are effectively lending it your money to do with as it pleases until you want it back.
Therefore the savings rate is what the bank pays you for borrowing your money.
An example with savings
How much will you make by saving £1k at 5% for nine months?
Another simple sum to start. If you saved this for a year, you'd earn £50 (5% of £1,000), but as you've only got the money there for nine months you'd actually get around three quarters of this, which is £37.50. Again this isn't exact due to compound interest.
Thankfully there's no tax on borrowing money, you simply pay back what you owe and the government doesn't get its hands on it.
Yet when you earn money from savings the interest earned counts as 'income', so you may have to pay income tax on it. The amount you pay depends on how much you earn in total – adding up employment and savings income.
Personal savings allowance
Since 6 April 2016, the personal savings allowance (PSA) has meant that every basic-rate taxpayer can earn £1,000 interest per year without paying tax on it (higher-rate £500). See below for the tax rates if you earn more interest than your PSA.
10% rate tax
The 10% rate has been abolished since the 2015/16 tax year. See more on the Tax-Free Savings that replaced it.
People who pay the basic (or intermediate in Scotland) rate of tax (roughly those who earn between £12,500 and £50,000 – or £43,430 if you live in Scotland – in 2020/21) and earn more than their PSA will pay 20% (or 21% for some in Scotland) of their savings income in tax, the same level as on employment income.
Those who pay the higher rate of tax (roughly those who earn between £50,000 – or £43,430 if you live in Scotland – and £150,000 in 2020/21) pay 40% (41% in Scotland) on both.
- Additional-rate tax
In the 2020/21 tax year anyone whose salary tops £150,000 will pay additional tax at a 45% rate (46% in Scotland).
Those who don't pay any income tax (roughly those whose income is under £12,500 in 2020/21) don't pay any tax on savings. This usually includes students and children, who are taxed like anyone else, but rarely earn over the threshold.
For more information on personal allowances and rates, read the Tax Rates guide.
One quick tip - married partners can give each other money without any tax impact. Therefore, if one of you is on a lower tax band, putting the savings in their name should mean you pay less tax on the interest earned. Although only ever do this if you're in a trusting relationship.
How compound interest works
This is a really important issue - a core building block of everything to do with saving and borrowing. So hopefully we can explain it clearly.
Suppose you had £1,000 in a savings account which paid 10% annual interest after tax (if only!). After year one you'd have £1,000 plus £100 interest (10% of £1,000), a total of £1,100. After year two, you'd earn another £100 interest (the interest on the original £1,000), plus a further £10 of interest earned on the £100 interest from the first year. So now you'd have a total of £210.
By year three, you'd be earning interest on the interest from year two, and interest on the interest on the interest from year one (gulp). Basically, that's what compounding is all about.
Hopefully the graph above will make this all clear.
All this means that the money grows more quickly because you don't just earn interest on the money you originally save, you also earn interest on the interest. This makes a big difference.
The longer you save for, the greater the effect of compound interest.
Let's say you put that money away for 20 years. If you were only earning the £100 a year, without the compounding, you'd have £3,000 in the bank afterwards. However because of the interest on the interest, you'd actually have £6,700.
Remember this accelerates debts too!
Borrow money and as well as paying interest on the original borrowing, you pay interest on the interest accrued. Therefore...
The longer you borrow for, the quicker your debts grow.
Sadly, compound interest tends to have an even bigger impact on debts than on savings, because interest rates are higher. Borrow £1,000 at 15% over 20 years without making any repayments, and you'd owe a massive £16,400 (without compound interest it'd be £4,000).
Rough compound interest calculation rule of thumb for maths nerds: Divide 72 by the annual interest rate and that's approximately how long it takes debts to double, so 72 divided by 9% equals 8 years. This starts to get less accurate for rates over 20%.
What is APR?
Right, now we're going to get a little bit technical. APR stands for the Annual Percentage Rate, and it's the official rate used for borrowing. When it's calculated it has to include:
- The cost of the borrowing, so the amount of interest charged plus
- Any associated fees that are automatically included, such as an application or annual fee
An APR is therefore meant to give you the overall equivalent cost of a debt, which you can then use to compare against other credit and loan products. It must be displayed by a lender before any agreement is signed.
The fact it includes charges sometimes means the APR can be a bit confusing. For example, an interest rate could be 22.2% per annum but the APR is 27.3%, as the impact of a £25 annual fee adds the equivalent to another 5.1% interest. Yet this is useful as it allows a true comparison.
Beware banks quoting monthly interest
Often if a credit card company ups the interest it charges, the letter informing you will express this in monthly terms. This makes it sound significantly smaller, yet 2% monthly interest is a whopping 27% APR. Due to compounding, it's not as simple as multiplying by 12 to work this out though, so to help we've built a special calculator to show you the real rate (if you are reading this on your mobile you need to go to the desktop version to see and use the calculator).
The Interest Rate Converter
Plug in the interest rate on your statement and choose whether you want to convert from "monthly to yearly" or vice versa. Click "Go!" and the converter will switch your interest rate into the one you requested.
Problems with the APR rate
While it all sounds good so far, unfortunately there are a number of problems with APR. Here are three of the main things to watch for.
It doesn't make sense with changing rates
The APR is meant to indicate the amount you will pay each year over the full term of the debt. Yet when rates change this can make it more rather than less complicated.
Mortgages are the best example. The APR is calculated by taking the total interest cost over the 25-year term of the mortgage, plus fees. This figure must be included prominently in mortgage adverts and brochures.
Yet what does it mean practically? A mortgage could tout 6.6% APR, yet you may never be charged 6.6%; instead you get a 4.5% fixed rate for two years followed by 6.75% variable for the remainder of the term. The 6.6% is the average cost if you were in the unlikely situation of keeping that mortgage for the full 25-year term, not a very useful figure.
For more details read Martin's blog on why you should 'Ignore mortgage APR rates, they're a meaningless load of b...aloney'.
You won't necessarily get the advertised APR
So far we've explained what APR means. However, where the term 'representative APR' is used, this means 51% of successful applicants will be given the advertised interest rate. The rest will most likely get a higher rate.
With credit cards, the rate for purchases (as opposed to balance transfers or cash withdrawals) is used as the main rate to advertise the card.
So if that is described as 19.9% representative APR, then 51% of people accepted have to get 19.9% APR, but the other 49% could be offered a different rate (likely to be higher).
Loans are slightly simpler as they only have one rate. So if a loan is advertised as being 7.5% representative APR, this means 51% of accepted applicants have to get 7.5%, and up to 49% could be offered a different rate (likely to be higher).
Of course, some people will be rejected outright for the card or loan too.
It only includes compulsory charges
Get a loan and some lenders will automatically include payment protection insurance in the quote. Technically this is voluntary, but you usually need to opt out (and you should do – read the Cheap Loans article). Yet while we're pushed to get the insurance, as it isn't compulsory, its cost isn't included in the APR.
Therefore some lenders deliberately load the cost of the insurance policies and make the loan rate cheaper. This means that with payment protection insurance a 6.7% APR loan can cost more than a 8% APR loan, as the latter has much cheaper insurance.
What is AER?
The AER, or Annual Equivalent Rate, is the official rate for savings accounts, and is designed to allow easy comparisons as it's meant to smooth out the variances between accounts (it's the equivalent of the APR for debts).
The idea is it shows what you'd get over a year if you put money in the account and left it there. The alternative is the gross rate, which is the flat rate of interest that's actually paid.
Frankly this next bit is about to get seriously complicated, so unless you're finding it all crystal clear so far, I'd skip it. If you don't read on, just remember the real lesson is ‘always compare like with like, thus AER with AER or gross with gross.'
Both these rates are usually quoted before tax, but there are two main areas where the difference shows:
Monthly or yearly interest?
If interest is paid annually then the gross rate and AER should be the same, as there's no interest compounding.
Yet when interest is paid monthly, then the gross rate given is usually around 0.1% less than the AER rate. This is because if the monthly interest was left in the account, then there would be interest on the interest too. The AER makes sure this is included.
For an identical account, if interest was paid monthly it would be a 4.89% gross rate, but if interest was paid annually it would be 5% gross. Leave the money there over a year, though, and both would receive the same amount, as the AER for both is 5%.
Bonus rates of interest
The second confusion is the impact of bonus interest rates. If a bonus is being paid for six months, then the AER (which stands for Annual Equivalent Rate remember), would be less than the gross rate for the first six months as it would need to incorporate the period pre- and post-bonus.
However, if you're planning to shift accounts when the bonus rate ends, then the AER is irrelevant, as you only want to know the interest rate during the bonus period. So, in this case, you should switch rates and compare gross (and take note of whether it's monthly or yearly interest!)
Watch out for flat interest rate loans
Well, we slagged off APRs earlier, but there's a much worse measure out there. It's sometimes used by car dealers trying to make car finance loans sound cheaper, but - thankfully - this is becoming less and less common.
If the three little letters A, P and R don't follow the rate of a personal or car loan… danger! APRs automatically mean the rate is charged on any outstanding debt. Borrow £5,000 over 5 years and by the last year you only pay interest on the amount remaining, say £1,000. At 6% APR the total interest is £800.
With a flat rate the interest is charged on the original amount borrowed, no matter what's been repaid, so in the last year you still pay interest on the whole £5,000. With a 6% flat rate, the total interest is £1,500.
Hence 6% sounds cheap but is roughly equivalent to a costly 12% APR. So if the salesman's given you an interest rate, before you sign any credit agreement, always check the rate that's mentioned on there - it's illegal for consumer credit agreements not to have the APR on them.
See our guides to car finance for more information on the different finance options you could be offered in a car showroom.