Compound interest explained: formula and examples

Compound interest means earning interest on both your original balance and interest already added to it. The effect builds over time when you leave those earnings in the account. An investment model can illustrate the same reinvestment principle, although investment returns are uncertain and can be negative.

A simple two-year example

Start with £1,000 and assume 5% interest, added once a year. After year one, the balance is £1,050. In year two, 5% applies to £1,050, producing £52.50 rather than £50. The balance becomes £1,102.50. These are hypothetical numbers, not an available savings offer.

Enter 5% as 0.05 in that formula. It assumes annual compounding and no money added or withdrawn. Changing the compounding frequency changes the calculation.

What changes with monthly contributions?

Each contribution has its own time to grow. A payment at the end of month one compounds for longer than the final payment. Our calculator treats the entered annual rate as a nominal rate, divides it by 12, and adds contributions at each month end. Do not substitute an advertised annual equivalent rate without checking how it should be converted.

Try £1,000 initially, £100 monthly, 5% nominal annual interest and ten years. The illustration produces about £17,175.24. Of that, £13,000 is money you contributed and approximately £4,175.24 is modelled growth. At 0%, the same payments total exactly £13,000.

Use a range of assumptions

Run the same calculation at 0%, 3% and 5% and compare the results. This is a sensitivity exercise, not a probability forecast. Fees, tax, inflation and withdrawals can reduce the amount available to spend. A smooth assumed rate also hides the ups and downs of an investment portfolio.

Common question: is more frequent compounding always better?

For the same positive nominal rate, more frequent compounding produces a higher effective annual rate. But compare actual products on a consistent basis: a lower nominal rate with monthly compounding is not automatically better than a higher rate compounded annually.