What Is Compound Interest and Why Does It Matter?
Compound interest is interest calculated on your original amount plus all the interest already earned. Simple interest, by contrast, is calculated only on the original amount.
Over short periods the difference is small. Over long periods it becomes the main driver of the result.
A worked comparison
Put 1,000 away at 10 per cent a year.
| Year | Simple interest | Compound interest |
|---|---|---|
| 1 | 1,100 | 1,100 |
| 5 | 1,500 | 1,611 |
| 10 | 2,000 | 2,594 |
| 20 | 3,000 | 6,727 |
| 30 | 4,000 | 17,449 |
At thirty years, compounding produces more than four times the simple interest result from the same deposit and the same rate. Nothing changed except that interest was allowed to earn interest.
The formula
A = P(1 + r/n)^(nt)
- A is the final amount
- P is the starting amount
- r is the annual rate as a decimal, so 5 per cent is 0.05
- n is how many times a year interest is compounded
- t is the number of years
Example: 5,000 at 6 per cent compounded monthly for 10 years.
A = 5000(1 + 0.06/12)^(12 x 10) = 5000(1.005)^120, which is approximately 9,097.
The same money at simple interest would reach 8,000.
Compounding frequency
More frequent compounding produces more, though with diminishing returns. 10,000 at 5 per cent for one year:
- Annually: 10,500.00
- Quarterly: 10,509.45
- Monthly: 10,511.62
- Daily: 10,512.67
This is why advertised rates can mislead. The figure that allows comparison is the annual equivalent rate, which folds compounding frequency in.
The rule of 72
Divide 72 by the annual rate to estimate how many years it takes to double.
- At 2 per cent: about 36 years
- At 6 per cent: about 12 years
- At 9 per cent: about 8 years
It is an approximation, and accurate enough for mental arithmetic in the range of rates most people encounter.
Why starting early beats saving more
This is the part worth internalising.
Person A saves 200 a month from age 25 to 35, then stops. Ten years of contributions, 24,000 total.
Person B saves 200 a month from age 35 to 65. Thirty years of contributions, 72,000 total.
At 7 per cent, by age 65 Person A typically ends up with more, despite contributing a third as much. The early money had thirty extra years to compound.
Time matters more than amount, which is an uncomfortable message for anyone starting late and a compelling one for anyone starting now.
When it works against you
Compound interest on debt works identically and in the wrong direction.
Credit cards commonly compound daily at rates around 20 per cent or higher. Paying only the minimum means interest is charged on interest, which is how balances persist for years.
Paying off a 20 per cent debt is mathematically equivalent to a guaranteed 20 per cent return, which is far better than most investments offer. That is why clearing expensive debt usually comes before investing.
Inflation interacts with all of this, since it erodes the real value of returns. See our explainer on what inflation is.
Where compounding shows up in everyday life
It is easy to treat this as a savings topic. In practice the same arithmetic runs underneath several ordinary decisions.
Mortgages
A mortgage is compound interest in reverse, spread over decades. Early payments are mostly interest and barely touch the balance, which is why overpaying in the first years has an outsized effect. A small regular overpayment can remove years from the term, because every unit of principal cleared early stops accruing interest for the whole remaining period.
Pension contributions
Workplace pensions combine compounding with employer matching, which acts as an immediate return before any growth. Declining a match is one of the few genuinely free losses available in personal finance.
Fees
Fees compound too, and this is the part most people underestimate. An annual fee of one per cent against 0.2 per cent sounds trivial. Over thirty years it can consume a fifth or more of the final balance, because the money taken in fees also stops compounding.
When comparing two funds with similar strategies, the lower ongoing charge wins more often than not, for this reason alone.
Buy now, pay later and credit
Short term borrowing often advertises a modest monthly figure rather than an annual rate. Converting it to an annual equivalent usually produces a much larger number, and if the balance rolls over, compounding does the rest.
A quick way to sanity check any offer
- Find the annual equivalent rate, not the headline rate.
- Subtract inflation to get the real return.
- Subtract any annual fee.
- Apply the rule of 72 to what is left.
If the doubling time that comes out is longer than you expected, the headline rate was doing more marketing than mathematics.
Frequently asked questions
What is the difference between APR and APY?
APR is the simple annual rate without compounding. APY includes compounding, so it is higher. Loans are usually advertised as APR and savings as APY.
How often do savings accounts compound?
Commonly daily or monthly, with interest credited monthly. The terms will say.
Does compound interest apply to investments?
Similar growth happens through reinvested dividends and gains, though returns vary year to year rather than being fixed.
Is compound interest ever bad for savers?
No, but it can be outpaced. If inflation exceeds your rate, the balance grows while purchasing power falls.
What is continuous compounding?
A theoretical limit where compounding happens constantly, calculated as A = Pe^(rt). It is used in finance mathematics, and the difference from daily compounding is tiny.
How do I work out the rate I need?
Rearrange the formula, or use the rule of 72 in reverse: to double in 9 years, you need roughly 8 per cent.
This article is general information, not financial advice.
