Compound Interest Calculator
Compounding is interest earning interest. Over short periods it is barely noticeable; over decades it does most of the work.
The formula
For a lump sum the standard compound interest formula is:
Regular contributions need a second term, the future value of an annuity:
This calculator computes both and adds them. It converts the compounding frequency into an equivalent monthly rate first, so a monthly contribution compounded daily is handled correctly rather than approximated.
A worked example
£5,000 invested at 6 % compounded monthly for 20 years, with £200 added every month:
- The lump sum: 5,000 × (1 + 0.06÷12)^(12×20) = 5,000 × 1.005^240 = £16,551.
- The contributions: 200 × ((1.005^240 − 1) ÷ 0.005) = £92,408.
- Total: £108,959, of which £53,000 was paid in and £55,959 is growth.
The revealing detail is the timing. After 10 years the balance is about £41,600 and only £8,600 of that is growth. In the second decade, growth alone adds more than everything the first decade produced. This is the shape of every compounding curve, and it is why starting early beats contributing more.
Why compounding frequency matters less than you think
At 6 % on £10,000 for one year:
| Compounded | Balance after 1 year | Effective rate |
|---|---|---|
| Annually | £10,600.00 | 6.000 % |
| Quarterly | £10,613.64 | 6.136 % |
| Monthly | £10,616.78 | 6.168 % |
| Daily | £10,618.31 | 6.183 % |
| Continuously | £10,618.37 | 6.184 % |
The gap between annual and daily compounding is £18 on £10,000. The gap between a 6 % rate and a 6.5 % rate is £50. Rate matters roughly three times more than frequency, so compare the effective annual rate (AER or APY) rather than being impressed by “daily compounding” in marketing.
What this calculation ignores
The arithmetic is exact. The forecast is not, because three things sit outside it:
- Inflation. £108,959 in twenty years will not buy what it buys today. At 2.5 % inflation its purchasing power is about £66,500 in today's money. A real return is the nominal rate minus inflation.
- Tax. Interest and gains may be taxable depending on the account and your jurisdiction. Tax-sheltered accounts change the outcome materially.
- Volatility. This model assumes a constant rate. Real investment returns are not constant, and the order in which good and bad years arrive affects the outcome when you are contributing or withdrawing — a risk that a smooth curve completely hides.
Use it to understand the shape of compounding and to compare scenarios, not as a prediction of a specific future balance.
Frequently asked questions
What is the rule of 72?
A shortcut for doubling time: divide 72 by the annual percentage rate. At 6 %, money doubles in roughly 72÷6 = 12 years. It is accurate to within a few months for rates between about 4 and 12 %. There is a dedicated rule of 72 calculator on the site.
Is it better to invest a lump sum or spread it out?
Historically, investing a lump sum immediately has beaten spreading it out about two thirds of the time, simply because markets rise more often than they fall. Spreading it reduces the regret risk of investing everything just before a fall, which is a behavioural benefit rather than a mathematical one.
Does this account for fees?
No. Enter a rate net of fees if you want a realistic figure. A 1 % annual charge on a 6 % gross return is not a 1 % reduction in the outcome — over 30 years it removes roughly a quarter of the final balance, because the fee compounds too.