Simple vs. compound interest
Simple interest is calculated only on the original principal: I = P × r × t, where P is principal, r is the annual rate, and t is time in years. £1,000 at 5% simple interest for 10 years earns £500 in interest, giving £1,500 total.
Compound interest applies the rate to the growing balance rather than the original principal. The same £1,000 at 5% compounded annually for 10 years gives: A = 1,000 × (1 + 0.05)^10 = £1,628.89 — roughly 26% more than simple interest over the same period. The longer the time horizon, the greater the divergence.
The compound interest formula
The standard formula is A = P × (1 + r/n)^(n×t), where A is the final amount, P is the principal, r is the annual interest rate (as a decimal), n is the number of compounding periods per year, and t is time in years.
For £1,000 at 6% compounded monthly (n = 12) for 5 years: A = 1,000 × (1 + 0.06/12)^(12×5) = 1,000 × (1.005)^60 ≈ £1,348.85. The same deposit compounded annually (n = 1) gives £1,338.23 — a small but real difference from compounding frequency alone.
Compounding frequency: does it matter?
In principle, more frequent compounding means slightly more growth. Annual, quarterly, monthly, and daily compounding all produce different final amounts, though the difference between monthly and daily is very small at typical savings rates.
The theoretical limit of more and more frequent compounding is continuous compounding: A = P × e^(r×t), where e is Euler's number (~2.718). For most practical purposes — comparing ISA rates, savings accounts, or loan APRs — monthly compounding is the most common standard in the UK, and annual compounding is common in the US. Always check the effective annual rate (EAR) rather than the nominal rate when comparing products.
The Rule of 72
The Rule of 72 is a mental shortcut for estimating how long it takes to double your money. Divide 72 by the annual interest rate: at 6%, your money doubles in approximately 72 ÷ 6 = 12 years. At 9%, it doubles in about 8 years. The rule is accurate to within a year or two for rates between 6% and 10%.
This same rule applies in reverse to debt. Credit card balances at 20% annual interest double in roughly 3.6 years if unpaid. Understanding the doubling time is a useful gut-check when evaluating any financial product with an interest component.
Regular contributions
Lump-sum compound interest is powerful, but regular contributions amplify it further. Adding a fixed amount each month or year while the balance compounds creates a savings trajectory that grows exponentially over long horizons — this is the mathematical basis for pension contributions, ISAs, and index fund investing.
Our compound interest calculator supports both lump-sum and regular contribution scenarios so you can model realistic savings plans rather than theoretical single deposits.