Build intuition for how compound interest grows savings and debts over time with worked examples.
You invest £5,000 at 5% per year, compounded monthly, for 3 years. What is the final balance?
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Compound interest is one of the most powerful — and most underestimated — concepts in personal finance. When interest is added to a balance and that enlarged balance earns interest in the next period, growth is no longer linear but exponential. Over long time horizons the difference between compound and simple interest becomes very large.
The formula is A = P(1 + r/n)^(nt), where P is the principal (starting amount), r is the annual interest rate expressed as a decimal (e.g. 4.5% = 0.045), n is the number of times interest compounds per year, and t is the number of years. Annual compounding (n = 1) gives the smallest balance for a given rate; monthly compounding (n = 12) gives the largest, because interest is credited more frequently and starts earning sooner.
In the UK, most easy-access savings accounts and Cash ISAs compound monthly. Fixed-rate bonds often compound annually. Credit-card debt compounds daily in many cases, which is why balances grow so quickly if you carry debt month to month.
This drill generates questions with principals between £1,000 and £20,000, annual rates between 2% and 6%, and time periods of 1 to 10 years. All three compounding frequencies (annual, quarterly, monthly) appear. The formula reference panel above the question can be expanded at any time as a memory aid.
A useful rule of thumb is the Rule of 72: divide 72 by the annual interest rate to estimate how many years it takes to double the investment. At 4%, money doubles in roughly 18 years (72 ÷ 4). This only works for annual compounding, but it gives a good intuition for the power of compound growth.
Savings context: as of 2026, UK easy-access savings accounts are paying around 4–5% AER. The AER (Annual Equivalent Rate) always assumes annual compounding, making it easy to compare accounts that compound at different frequencies.
A = P(1 + r/n)^(nt), where P is principal, r is annual rate as a decimal, n is compounding frequency per year, and t is years.
Simple interest is always calculated on the original principal. Compound interest is calculated on the growing balance, so you earn interest on your interest. Over many years the difference is enormous.
Most UK savings accounts and Cash ISAs compound monthly. Fixed-rate bonds usually compound annually. The AER (Annual Equivalent Rate) normalises all frequencies to an annual figure for fair comparison.
Divide 72 by the annual interest rate to estimate how many years it takes to double your money. At 6% it takes about 12 years (72 ÷ 6). At 3% it takes about 24 years.
Because interest is credited to the balance sooner, and that credited interest starts earning interest itself earlier. Monthly compounding earns slightly more than quarterly, which earns slightly more than annual — all at the same nominal rate.
AER (Annual Equivalent Rate) is the effective annual rate after compounding. It converts any compounding frequency into a single comparable annual figure. A 4.8% nominal rate compounded monthly has an AER of about 4.91%.
Credit card debt compounds daily in many cases. If you only pay the minimum each month, the outstanding balance grows faster than you expect because interest is charged on interest. This is why carrying a credit card balance is so costly.
Cash ISAs (tax-free interest) and fixed-rate bonds typically offer the best rates. Always compare AER, not the headline rate, to account for compounding frequency.
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