Compound Interest Calculator
Project the future value of a deposit (with optional regular contributions) at any rate, term, and compounding frequency — the universal time-value-of-money formula.
Final balance
£16,470.09
- Total contributed
- £10,000.00
- Interest earned
- £6,470.09
- Interest as % of contributions
- 64.7%
Compound interest is calculated as FV = P·(1+r/m)^(n·m) + PMT·((1+r/m)^(n·m) − 1) / (r/m), where m is the number of compounding periods per year. Daily compounding (m=365) gives a slightly higher result than monthly (m=12) at the same nominal rate.
How to use this calculator
Enter the initial principal, any regular contribution made each compounding period (leave at 0 for a pure lump-sum projection), the annual interest rate, the number of years, and how often interest is compounded. The result updates as you type.
How the calculation works
Uses the standard time-value-of-money formula: FV = P·(1+r/m)^(n·m) + PMT·((1+r/m)^(n·m) − 1) / (r/m), where P is the initial principal, PMT is the regular contribution, r is the nominal annual rate (as a decimal), m is the number of compounding periods per year, and n is the number of years. The 'regular contribution' is added each compounding period — so if you choose monthly, it's added every month; daily, every day; annually, once a year.
Worked example
Starting with £10,000, no further contributions, at 5% annual interest compounded monthly for 10 years: m=12, r=0.05/12, n=120. FV = 10,000 × (1 + 0.05/12)^120 ≈ £16,470. Total interest earned = £6,470 on £10,000 contributed.
Frequently asked questions
What is compound interest?
Compound interest is interest earned not just on your original principal, but also on the interest that has already been added to the balance. Each compounding period, the new balance becomes the basis for the next period's interest, so growth accelerates over time. Albert Einstein reputedly called it "the eighth wonder of the world" — whether or not he actually said it, the maths is genuine.
Does compounding frequency really matter?
A little, but less than most people think. At a 5% nominal rate over 10 years on £10,000, annual compounding gives £16,289, monthly gives £16,470, daily gives £16,486. The gap between monthly and daily is small because compounding has diminishing returns as m increases — the limit is continuous compounding (FV = P·e^(r·n)), which gives £16,487 in this example.
What is the difference between nominal rate and effective rate?
The nominal rate is the headline annual rate — what most savings accounts quote. The effective annual rate (EAR or APY) is what you actually earn after compounding. With a 5% nominal rate compounded monthly, the effective rate is (1+0.05/12)^12 − 1 = 5.116%. This calculator takes a nominal annual rate and applies the chosen compounding frequency.
Does this calculator account for inflation or tax?
No. The result is the nominal future balance — the actual number of pounds, dollars, or euros at the end. To see real purchasing power, subtract your expected inflation rate from the rate you enter (e.g. 4% instead of 6% if inflation is 2%). For tax, the result assumes growth is sheltered (e.g. inside an ISA, 401(k), or pension); if held in a taxable account, deduct your marginal rate from each period's interest.
How is "regular contribution" applied?
It's added at the end of each compounding period (an "ordinary annuity"). So with monthly compounding and a £100 monthly contribution, £100 is added at the end of each month and earns interest from the next month onward. The first contribution earns interest for n−1 periods; the last contribution earns nothing. This is the standard convention used by spreadsheet FV() functions.
Why does my answer differ from another online calculator?
The two most common reasons are timing (contribution at the start of each period vs. the end) and frequency mismatch (some calculators always use monthly compounding even when you select annual). This calculator uses end-of-period contributions and applies your selected compounding frequency to both the lump sum and the contributions, matching the spreadsheet =FV() convention.