Compound Interest Calculator
Future value, total interest, and growth from compound interest with optional regular contributions
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What this calculator computes
The compound-interest calculator projects the future value of a savings account, investment, or pension contribution under a stated annual return rate, with adjustable compounding frequency and an optional schedule of regular monthly or annual contributions. The base formula for compounding without contributions is FV = P × (1 + r/n)^(nt), where P is the principal, r is the annual return rate as a decimal, n is the number of compounding periods per year, and t is the number of years. Adding regular contributions extends the formula with an annuity term: FV = P × (1 + r/n)^(nt) + PMT × [((1 + r/n)^(nt) − 1) / (r/n)] × (1 + r/n × type), where type indicates whether contributions are made at the start (1) or end (0) of each period. Compound interest is the engine behind long-term wealth building: a £200 monthly contribution at 7% compounded monthly grows to £242k over 30 years, of which £72k is contributions and £170k is investment growth — the famous "money makes money" effect that justifies starting retirement saving in your 20s rather than your 40s. The calculator returns the future value, the total contributions, and the cumulative interest earned, plus a year-by-year balance projection so the curvature of the growth curve is visible. **Educational tool only — not financial advice. The calculator assumes a constant return rate; real-world investment returns are volatile, fees and taxes reduce net returns by 0.5–2% per year, and inflation erodes purchasing power by 2–4% per year. Consult a qualified financial advisor before making investment decisions, particularly for retirement planning.**
Calculator
The formula
Formula
FV = P × (1 + r/n)^(nt) with PMT: + PMT × [((1+r/n)^(nt) − 1) / (r/n)]
Worked example
When to use this calculator
Use this calculator for any long-horizon savings or investment projection — pension contributions, ISA savings, taxable brokerage portfolios, education-fund saving for children, or sinking funds for major future purchases (house deposit, car replacement, retirement). The calculator's strength is in showing the asymmetric power of long compounding periods: a £100 monthly contribution at 7% over 40 years grows to £262k, while the same £100/month over 20 years grows to only £52k — fivefold more from doubling the time horizon, illustrating why early saving matters more than larger later contributions. Use realistic return assumptions: 5–7% real return is the long-term historical average for diversified equity portfolios after inflation, while 3% is a reasonable bond-heavy assumption. Account for fees by reducing the input rate by your platform's annual charge (typically 0.2–0.5% for index funds, 1–2% for actively managed funds). The calculator does not handle variable contribution rates, scheduled withdrawals, tax-sheltered vs taxable accounts, or sequence-of-returns risk in early retirement.
Common input mistakes
- Using nominal returns rather than real returns. A 7% nominal return at 3% inflation is only a 3.9% real return; over 30 years the real spending power of the FV is far less than the nominal figure suggests. For retirement-planning purposes, enter the real rate (nominal minus inflation) so the projected balance is in today's pounds; for nominal-balance projections (matching what the brokerage statement will say), use the nominal rate.
- Ignoring fees in the rate input. A 7% gross return on a fund with a 1.5% expense ratio is actually 5.5% net to the investor, and over 30 years the difference compounds dramatically: 7% turns £200/month into £244k, while 5.5% turns the same contributions into £172k — a 30% reduction from a 1.5% fee difference. Always subtract the platform expense ratio from the input rate to project net-of-fees growth.
Frequently asked questions
What is compound interest?
Compound interest is interest earned on previously-earned interest, in addition to interest on the original principal. With simple interest, a £1000 deposit at 5% earns £50 per year regardless of accumulated value; with compound interest, the same deposit earns £50 in year 1, £52.50 in year 2 (5% of £1050), £55.13 in year 3, and so on, growing exponentially over time. The longer the time horizon, the more dramatically compound interest dominates simple interest — Einstein reportedly called it "the eighth wonder of the world".
How often should interest compound?
Compounding frequency increases the effective annual rate slightly: 7% compounded annually gives an effective rate of 7%, while 7% compounded monthly gives 7.23%, daily gives 7.25%, and continuously gives 7.25%. The differences matter mostly for short-horizon high-rate scenarios; over decades the difference between monthly and daily compounding is negligible compared to the difference between, say, 6% and 7% annual rates. Most savings accounts compound daily; investment funds notionally compound continuously through stock-price appreciation.
How much do small contributions grow over time?
£100 per month at 7% over 40 years grows to £262,481, of which £48,000 is contributions and £214,481 is growth. Doubling the contribution to £200/month and the result becomes £524,963 (linear with contribution). Halving the time horizon to 20 years shrinks £100/month to £52,397, of which £24,000 is contributions and £28,397 is growth — much less dramatic. Time matters more than contribution size at long horizons, which is the central argument for starting pension contributions in your 20s.
What return rate is realistic?
Long-term historical UK and US equity-market returns are about 7% per year nominal (4–5% real, after inflation), with significant year-to-year volatility (the FTSE All-Share has had single-year returns from −33% to +42% over the past 30 years). Diversified bond portfolios return 3–5% nominal long-term. Cash savings currently return 4–5% on the best instant-access accounts in the UK (2024–25 levels) but are typically below inflation in normal-rate environments. Use 5–7% nominal for long-horizon equity-heavy projections, 3–4% for bond-heavy.
Are these projections accurate?
No — the calculator assumes a constant return rate, while real-world returns are volatile and the order in which the returns occur matters (sequence-of-returns risk). Two portfolios with the same average return can have very different end balances depending on whether the bad years come early or late in the contribution period. The calculator's projections are useful for understanding the magnitude of compound growth and for comparing scenarios, but should not be treated as predictions. Use Monte Carlo simulation tools for realistic retirement-planning projections.