What Is Compound Interest, Explained Simply?
Compound interest is interest earned on interest, and over long periods it dominates everything else. A plain explanation with numbers, and why it cuts both ways.
In short
Compound interest is interest calculated on the original amount plus all the interest already added, so growth accelerates over time. At 5 percent a year, 1,000 becomes 1,050 after one year and 1,629 after ten, not 1,500, because each year's interest is earned on a larger base. The same mechanism makes debt grow faster the longer it is left.
Interest is what you are paid for lending money, or charged for borrowing it. Compound interest is what happens when that interest is added to the balance and starts earning, or costing, interest of its own.
That is the whole definition. What makes it worth an article is how badly human intuition handles it.
The numbers
Put 1,000 in an account paying 5 percent a year.
- After 1 year: 1,050
- After 2 years: 1,102.50, because the 5 percent applied to 1,050, not 1,000
- After 10 years: 1,629
- After 20 years: 2,653
- After 30 years: 4,322
Simple interest would give 2,500 after 30 years. Compounding gives 4,322. The gap between them is entirely interest earned on interest, and it grows every year.
Why intuition fails
We think in straight lines. Told that something grows 5 percent a year, we picture a steady slope. The reality curves upward, slowly at first and then steeply, and the final years contribute more than all the early years combined.
In the example above, the last ten years add 1,669. The first ten added 629. Same rate, same account.
The formula, for anyone who wants it
Final amount equals starting amount multiplied by one plus the rate, raised to the number of years. For 1,000 at 5 percent over 10 years: 1,000 × 1.05 to the power of 10, which is 1,629.
The exponent is where the power lives. Everything else is arithmetic.
Time beats rate
This is the practical consequence people miss. Because the curve steepens late, the number of years matters more than almost anything else.
Someone who saves 200 a month from 25 to 35 and then stops, leaving it to grow at 6 percent, ends up with more at 65 than someone who saves 200 a month from 35 all the way to 65. Ten years of contributions beats thirty, because the first ten had longer to compound.
Starting early with a small amount is not a consolation prize. It is the winning strategy.
It works against you just as hard
Debt compounds too, and credit card debt compounds daily. A balance of 3,000 at 22 percent with only minimum payments takes over twenty years to clear and costs more in interest than the original amount. Nothing about that is unusual. It is the same curve pointed the other way.
This is why the standard advice has the order it does: clear high-interest debt before investing. A guaranteed 22 percent by paying off a card beats any realistic return elsewhere.
The rule of 72
Divide 72 by the rate to get the doubling time. At 6 percent, money doubles every 12 years. At 2 percent, every 36. At a card’s 24 percent, every 3.
It is accurate within a few percent for rates under 15 or so, and it is the single most useful piece of mental arithmetic in personal finance, because it turns an abstract percentage into a number of years you can picture.
Common questions
How is compound interest different from simple interest?
Simple interest is paid only on the original amount, so 1,000 at 5 percent earns 50 every year forever. Compound interest is paid on the growing balance, so year two earns 52.50, year three 55.13 and so on. Almost all real savings and debt compound.
How often does it compound?
It depends on the product. Savings accounts usually compound monthly or annually; credit cards typically compound daily. More frequent compounding produces a slightly higher effective rate for the same headline figure.
How long does money take to double?
Divide 72 by the annual rate. At 6 percent, about 12 years; at 3 percent, about 24. The rule of 72 is accurate enough for any rate under about 15 percent.
Sources
Every factual claim above traces to one of these. Follow them rather than taking this article's word for it.
- Inflation calculator Bank of England
- Inflation and price indices Office for National Statistics
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