What compound interest is
Compound interest means interest is earned on both the original amount and the interest already added. It is interest on interest. Over short periods the effect can look small, but over long periods it can become very powerful.
Compound interest applies to savings accounts, investments, pensions, loans, credit cards, and many other financial products. It can work for you when returns are reinvested, and against you when debt interest is added to an unpaid balance.
Simple vs compound interest
Simple interest is calculated only on the original principal. Compound interest recalculates from the growing balance. If GBP 1,000 earns 5% simple interest for two years, the interest is GBP 50 each year. With annual compounding, year two interest is calculated on GBP 1,050 rather than GBP 1,000.
Worked example
Suppose GBP 1,000 earns 5% per year for three years with annual compounding.
- Year 1: GBP 1,000 x 1.05 = GBP 1,050
- Year 2: GBP 1,050 x 1.05 = GBP 1,102.50
- Year 3: GBP 1,102.50 x 1.05 = GBP 1,157.63
The balance after three years is GBP 1,157.63, with GBP 157.63 of growth before tax or charges.
Compound interest formula
The standard formula is FV = PV x (1 + r)^n, where FV is future value, PV is starting value, r is the rate per period, and n is the number of periods. If regular contributions are added, the calculation also needs to include the future value of each contribution.
Compounding frequency
| Frequency | What it means | Effect |
|---|---|---|
| Annual | Interest added once per year | Simple to understand |
| Monthly | Interest added 12 times per year | Slightly higher effective annual return |
| Daily | Interest added daily | Usually only a small increase over monthly |
| Continuous | Mathematical limit of constant compounding | Mainly used for theory |
Why time matters
Time gives compounding room to work. Early growth creates a larger base for later growth. This is why starting earlier can sometimes matter more than trying to contribute a much larger amount later.
Inflation, tax, platform fees, fund charges, and investment volatility can all reduce real returns. A compound interest calculation is a scenario, not a promise.
Scenario example: regular monthly saving
A saver starts with GBP 2,000 and adds GBP 200 per month for 10 years. The account or investment grows at an assumed 5% per year before fees and tax. Each monthly contribution has its own compounding period, so earlier contributions grow for longer than later ones.
- Starting amount compounds for the full 10 years
- Month 1 contribution compounds for almost 10 years
- Final month contribution has almost no time to compound
- Total value is the starting pot growth plus the future value of all contributions
Regular contributions make compound growth less dependent on the starting amount. Time and consistency both matter.
Compound interest scenarios
| Scenario | Main driver | Risk or limitation |
|---|---|---|
| Cash savings | Interest rate and compounding frequency | Inflation can reduce real purchasing power |
| Pension investing | Contributions, tax relief, time, and investment return | Investments can fall as well as rise |
| Credit card debt | Unpaid balance and high interest rate | Compound interest works against the borrower |
| Mortgage overpayment | Avoided interest on a lower balance | Early repayment charges may apply |
| Long-term investing | Time in the market and reinvested returns | Returns are uneven and not guaranteed |
Common mistakes
- Confusing nominal return with real return after inflation.
- Ignoring fees and tax.
- Assuming investment returns arrive smoothly every year.
- Using annual rate but monthly periods without adjusting the rate.
- Forgetting that debt can compound too.
FAQ
What is the compound interest formula?
A common formula is FV = PV x (1 + r)^n.
Does monthly compounding beat annual compounding?
For the same nominal rate, more frequent compounding produces a slightly higher effective return.
Is compound interest guaranteed?
Only if the rate and product terms are guaranteed. Investments can rise or fall.
What is real return?
Real return adjusts nominal return for inflation.
Can compound interest work against me?
Yes. Debt interest can compound if unpaid interest is added to the balance.
This guide is for general information only and is not financial advice.