Compound interest calculator with working

• Savings: £1,000 at 5% a year for 3 years. Multiplier $= 1.05$. Amount $= 1000 \times 1.05^3 = £1157.63$, so the interest is £157.63.
• Depreciation: a £12,000 car loses 15% of its value each year. Multiplier $= 0.85$. After 2 years, $12000 \times 0.85^2 = £8670$.
• Monthly compounding: £1,000 at 12% a year compounded monthly for 1 year: $1000 \times 1.01^{12} \approx £1126.83$.

Raise the multiplier to the power of the number of years. This is much faster than working out each year separately.

Simple interest is paid on the original amount only, so it grows by the same amount each year. £1,000 at 5% simple interest for 3 years earns £150; compound interest earns £157.63. Over long periods the difference becomes large. For simple interest, use our simple interest calculator.

The same method models population growth, bacteria doubling and radioactive decay: any quantity changing by the same percentage each time period. Our exponential growth and decay questions practise these.

• Multiplying by 0.05 instead of 1.05 (that gives just the interest for one year).
• Using simple interest when the question says compound.
• Rounding each year instead of only at the end.

Practise with our compound interest questions and the percentage calculator.

• Read whether the question wants the final amount or just the interest.
• Give money to 2 decimal places.
• "Find the number of years until it doubles" questions: try increasing powers of the multiplier until the amount passes the target.

Try increasing powers of the multiplier. At 5% a year, $1.05^{14} \approx 1.98$ and $1.05^{15} \approx 2.08$, so money doubles during the 15th year. A quick estimate is the rule of 72: divide 72 by the percentage rate. $72 \div 5 = 14.4$ years, close to the real answer. At 8% it's about 9 years. The calculator's year-by-year table shows exactly when the amount first passes double.