Compound interest explained, with real numbers

Compound interest is interest earned on interest. That one idea explains why savings grow slowly and then quickly, why credit card debt gets out of hand, and why ten extra years can matter more than any choice of account.

Simple versus compound interest

With simple interest, you earn the same amount every year, calculated on the original sum. 10,000 at 5% earns 500 a year; after ten years you have 15,000.

With compound interest, each year's interest is added to the balance, and the next year's interest is calculated on the larger figure. The first year earns 500, the second 525, the third about 551, and so on. After ten years, compounded annually, the same 10,000 becomes about 16,289 — almost 1,300 more than simple interest, without any extra money paid in.

The formula

A = P × (1 + r ÷ n)^(n × t)

• P is the starting amount;
• r is the annual rate as a decimal, so 5% is 0.05;
• n is how many times a year interest is added;
• t is the number of years.

The Compound Interest Calculator applies this, adds regular contributions, and shows the balance year by year.

Does compounding frequency matter?

Less than advertising suggests. The same 10,000 at 5% for ten years:

Going from yearly to monthly adds about 181. Going from monthly to daily adds about 17. The rate and the time invested matter far more. This is also why savings accounts quote an effective annual rate — called APY in the US or AER in the UK — alongside the headline rate: 5% compounded monthly is equivalent to about 5.12% compounded once a year.

The rule of 72

Divide 72 by the annual percentage rate to estimate how many years it takes for money to double. At 6%, about 12 years; at 9%, about 8 years. The exact figures are 11.9 and 8.04, so the shortcut is close enough for planning. It works in reverse for debt and inflation too: at 3% inflation, prices double in about 24 years.

Regular contributions do the heavy lifting

For most people, the money they keep paying in matters more than the starting sum. Saving 200 a month at 7%, compounded monthly:

• after 20 years, you have paid in 48,000 and the balance is about 104,000;
• after 30 years, you have paid in 72,000 and the balance is about 244,000.

Ten more years of the same 200 a month adds 24,000 of contributions but about 140,000 to the balance. That is compounding at work, and it is the strongest argument for starting early, even with small amounts.

Fees compound too

A yearly fee comes straight out of the rate you earn, and it compounds just like the returns. The same 200 a month for 30 years grows to about 244,000 at 7%, but to about 201,000 at 6% — so a fee of one percentage point a year costs roughly 43,000, nearly a fifth of the final balance. Small differences in fees are worth comparing as carefully as differences in returns.

Remember inflation

A balance projected thirty years ahead is in future money. If prices rise by 2.5% a year, 244,000 in thirty years buys about what 116,000 buys today. That does not make saving pointless — it makes it necessary — but compare projections in today's money when you plan.

Compounding works against you on debt

The same mechanism makes unpaid debt grow. Credit cards typically charge interest on unpaid interest, at rates far higher than savings earn, so a balance left to roll over can grow quickly. Loans with fixed instalments work differently: each payment covers the interest due and reduces the debt — see how EMI is calculated. Paying off expensive debt is, in effect, a guaranteed return equal to its interest rate.

Using the calculator sensibly

• Use a realistic rate after fees, not the best year you have heard of.
• Remember investment returns vary from year to year; a fixed rate is a simplification.
• Try a few rates to see a range instead of a single answer.

This is a mathematical illustration, not investment advice. Investments can fall as well as rise, and a qualified adviser can help with decisions about your own money.