What is compound interest? Simple examples in pounds

The short answer: compound interest is interest on your interest. Each time interest is added to your savings, the next payment is worked out on the bigger balance. £10,000 at 4.5% grows to about £15,530 in 10 years with compound interest, against £14,500 with simple interest, and the gap widens every year.

Simple vs compound interest

With simple interest you earn 4.5% of the original £10,000, £450, every year. With compound interest you earn 4.5% of whatever the balance is now, which keeps growing:

After 30 years, compounding has more than doubled what simple interest would give. Time does most of the work, which is why starting early matters more than the rate.

The formula

Final amount = starting amount × (1 + rate)^years

For £10,000 at 4.5% for 10 years: 10,000 × 1.045¹⁰ = £15,530. If interest is added monthly, divide the rate by 12 and use months: 10,000 × (1 + 0.045 ÷ 12)¹²⁰ = £15,670, a little more.

Regular saving makes it work harder

Saving £200 a month at 4.5%:

After 30 years, more than half the total is interest. See how long it takes to save £10,000.

The rule of 72

To see roughly how long money takes to double, divide 72 by the rate:

AER, gross and APR: reading the rates

• Gross rate: the interest rate before tax, paid as often as the account says (monthly or yearly).
• AER (annual equivalent rate): what you would earn over a year with compounding included. Use it to compare savings accounts. An account paying 4.4% monthly has an AER of about 4.49%.
• APR: the yearly cost of borrowing, including fees. Compounding works against you here.

Inflation and tax

What matters is growth after inflation. At 4.5% interest with 3% inflation, your money's buying power grows by only about 1.5% a year. Interest outside an ISA can also be taxed once it goes over your Personal Savings Allowance; see do you pay tax on savings interest?

Compounding on debt

The same maths makes debt expensive. Unpaid credit card interest is added to the balance and charged interest itself. That is why minimum payments can take decades. See credit card interest explained.

Working it out by hand

£1,000 at 5% a year, with interest added once a year:

The interest grows each year because it is earned on the previous interest too. With simple interest, it would stay at £50 every year.

Why starting early matters

Saving £100 a month at 5% a year until age 65:

Starting ten years earlier adds only £12,000 of your own money but makes a much bigger difference to the final pot, because the early pounds have the longest to grow. Returns on investments are not guaranteed, but the same maths applies.

Where you meet compounding

• Savings accounts: interest paid monthly or yearly and left in the account compounds.
• Pensions and stocks and shares ISAs: reinvested growth and dividends compound over decades.
• Premium Bonds: prizes are paid out rather than added, so there is no compounding unless you reinvest them.
• Credit cards and overdrafts: unpaid interest is added to the balance and charged interest itself.

Examples are before tax and inflation unless stated. Savings rates change; check current rates before choosing an account.