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. But the basics is the most important bit!
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.
For example, if you borrowed £1,000 at an interest rate of 10% and paid it back six months later, this would cost you around £50. One year at 10% would cost you £100 (10% of £1,000), so over six months you'd pay about half that. It really is almost as simple as that.
The reason we 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.
Right, now we're going to get a little bit technical. APR stands for 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.
Only 51% need to get the representative APR, the rest could pay much more
The term 'representative APR' or 'rep APR' is widely used on credit card and loan adverts, yet this means only 51% of successful applicants must be given the advertised interest rate. The rest will most likely get a higher rate.
For example, if a loan is advertised as being 2.8% APR representative, this means 51% of accepted applicants have to get 2.8%, and up to 49% could be offered a different rate, which is often much higher. The same principle applies for credit cards, though this uses the interest rate for purchases, which can be different for other uses, such as balance transfers or cash withdrawals.
Of course, some people will be rejected outright for the card or loan too.
The longer you borrow for, the quicker your debts grow.
Borrow money and as well as paying interest on the original borrowing, you pay interest on the interest accrued. Sadly, this "compounding" of interest tends to have an even bigger impact on debts than on savings, because interest rates are higher.
For example, if you borrowed £1,000 at 15% over 20 years without making any repayments, 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 eight years. This starts to get less accurate for rates over 20%.
This is a much worse measure than APR. It's sometimes used by car dealers trying to make car finance loans sound cheaper, though this is much rarer now. 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 five 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 salesperson'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.
The interest rate when saving or in credit
This works in exactly the same way as for borrowing, 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. For example, if you saved £1,000 at 1% for nine months, you'd earn roughly £7.50. Over a full year you'd earn £10 (1% 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 £7.50. Again this isn't exact due to compound interest. See our Top Savings guide for more information.
When you earn money from most types of savings, the interest earned counts as 'income', so is liable for income tax on it. However in practice, less than 5% of people in the UK pay any tax on their savings due to the personal savings allowance (PSA), which means every basic-rate taxpayer can earn £1,000 interest per year without paying tax on it (higher-rate £500).
If you live in England, Wales or Northern Ireland £12,570 or less
No income tax payable £12,571 - £17,570
Up to £6,000 (ii) 20% £17,571 - £50,270
£1,000 20% £50,271 - £150,000
None 45% If you live in Scotland £12,570 or less No income tax payable £12,571 - £14,667 Up to £6,000 (ii) 19% £14,668 - £17,570 Up to £6,000 (ii) 20% £17,571 - £25,296 £1,000 20% £25,297 - £43,662 £1,000 21% £43,663 - £150,000 £500 41% Over £150,000 None 46%
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.
What about negative interest rates?
With rumours that negative interest rates could be on the way (where you'd actually lose money on your savings as you'd be paying a level of interest to keep them in an account), it's worth noting that HM Revenue & Customs has confirmed any 'loss' would not be taken off any other income. Instead this would be treated as a 'bank charge'.
So, for example, if you made £300 interest from one account (with a positive interest rate) but had to pay £100 due to a negative interest rate on another, £300 would still be considered as your income from interest.
This is a really important issue – a core building block of everything to do with interest rates. 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 below 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.
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:
Where interest is paid monthly
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%.
Where there's a bonus rate of interest for a limited time
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!)
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