Compound Interest Explained
Compound interest means the interest already added starts earning interest itself. The Compound Interest Calculator handles it with any compounding frequency.
Why the shape is backloaded
Invest 10,000 at 7 per cent compounded annually. The first year earns 700. The tenth year earns around 1,318 - on the same original 10,000 - because by then the balance is nearly 19,000.
After ten years you have about 19,672. After twenty, 38,697. After thirty, 76,123. The second decade adds more than the first, and the third adds more than both. Nothing changed except time.
That shape is the whole argument for starting early, and it is also why compounding feels disappointing for the first few years. Most of the growth happens in a period you cannot reach without first getting through the dull part.
Frequency matters less than people expect
Compounding can happen annually, monthly, daily or continuously, and more often is better for a saver. The gain is smaller than the fuss suggests.
10,000 at 6 per cent for ten years: annually gives 17,908, monthly 18,194, daily 18,221, continuously 18,221. The whole range from annual to continuous is about 1.7 per cent of the total.
Which is why the honest hierarchy is the rate first, the time second, and the frequency a distant third. A tenth of a per cent on the rate matters more than moving from monthly to daily compounding.
The figure that makes offers comparable is the effective annual rate, which folds frequency into one number - a nominal 6 per cent compounded monthly is an effective 6.17 per cent.
It works the same way against you
The mechanism is indifferent to which side you are on. A credit card at 22 per cent compounds monthly against your balance with exactly the arithmetic that works for a savings account, which is why a balance carried for years grows in a way that surprises people. The Credit Card Payoff Calculator shows that case specifically.
A quick estimate without a calculator
Divide 72 by the rate and you get roughly the years to double. At 6 per cent, about twelve years. At 9 per cent, about eight. It is accurate to within a few per cent for rates between about 5 and 12 - the Rule of 72 Calculator covers why it works.
One honest caveat about any projection: a fixed rate assumed over thirty years is a modelling assumption, not a forecast. Real returns vary, and inflation reduces what the end figure buys. A projection shows the arithmetic of compounding, not what will happen.
Common questions
What is the difference from simple interest?
Simple interest is charged on the original amount only - the Simple Interest Calculator covers it, and it is always cheaper for a borrower.
Does adding monthly contributions change the maths?
Yes, and substantially - each contribution starts its own compounding from the date it arrives.
Should I account for inflation?
For anything over a few years, yes. Subtracting expected inflation from the rate gives a figure in today's money.
Want to see how a balance grows?