See exactly how money grows with compound interest — daily, monthly, quarterly or annual compounding.
Calculate Compound Growth
£
Starting amount (leave at 0 if saving from scratch)
£
Optional: regular amount added each month
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Enter the AER shown on your account for accuracy
yrs
How often interest is calculated and added to your balance
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Final Balance
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Interest Earned
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Total Contributed
ContributionsInterest earned
Initial deposit
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Monthly contributions
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Total contributed
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Compound frequency
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Annual interest rate
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Time period
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Total interest earned
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How your result compares across compound frequencies
Year
Contributed
Interest
Cumulative Interest
End Balance
How Compound Interest Works
Simple Interest vs Compound Interest
With simple interest, you earn interest only on your original principal every period. £10,000 at 5% earns £500 per year regardless of how much interest has accumulated — producing £15,000 after 10 years.
With compound interest, each interest payment is added to the balance and then earns interest itself in subsequent periods. At 5% compounded annually, £10,000 becomes £16,289 after 10 years — £1,289 more than simple interest. Over 30 years at the same rate, the gap widens to over £17,000.
The Compound Interest Formula
Lump sum only:
A = P × (1 + r/n)n×t
With regular monthly contributions:
A = P × (1 + r_m)12t + PMT × [(1 + r_m)12t − 1] ÷ r_m
Where P = principal, r = annual rate, n = compounding periods per year, t = years, PMT = monthly contribution, r_m = effective monthly rate. The effective monthly rate accounts for the compounding frequency: for daily compounding, r_m = (1 + r/365)365/12 − 1.
The Rule of 72 — Doubling Your Money
Divide 72 by the annual interest rate to estimate the number of years it takes for a lump sum to double. This works for annual compound interest between roughly 4–15%:
3%
≈ 24 years
4%
≈ 18 years
5%
≈ 14.4 years
6%
≈ 12 years
7.2%
≈ 10 years
8%
≈ 9 years
10%
≈ 7.2 years
12%
≈ 6 years
Does Compound Frequency Really Matter?
On a typical UK savings rate of 5%, the difference between daily and annual compounding on a £10,000 lump sum over 10 years is just £198 (£16,487 vs £16,289). The impact is modest at low-to-medium rates. However, the gap widens significantly at higher rates and over longer periods — at 10% over 30 years, daily compounding produces around £5,000 more than annual compounding on £10,000.
In practice, UK savings accounts quote rates as AER (Annual Equivalent Rate), which already standardises for compounding frequency. Two accounts with the same AER will grow identically regardless of whether they technically compound daily or monthly. Enter the AER when using this calculator.
The Most Powerful Variable: Time
Starting 10 years earlier makes a far bigger difference than finding a higher rate. Consider £250/month at 5%:
Saving for 20 years: £60,000 contributed → £102,758 final balance (£42,758 interest)
Saving for 30 years: £90,000 contributed → £208,065 final balance (£118,065 interest)
An extra 10 years adds £105,306 to the final balance — more than the total contributions over 20 years. This is the compounding snowball in action: the later years produce the most interest because the balance is largest. Half of the 30-year interest is earned in the final decade.
What Is AER?
AER (Annual Equivalent Rate) is the standardised way UK savings products express their interest rate, accounting for how often interest compounds. If a savings account compounds monthly, the AER is slightly higher than the nominal monthly rate multiplied by 12. UK law requires all savings providers to display AER, making it straightforward to compare accounts on a like-for-like basis. Always use the AER figure shown on your account — not the "gross" or "nominal" rate — when entering values into this calculator.
Worked Examples
Three UK compound interest scenarios — all calculated with monthly compounding and end-of-period contributions.
James, 35 — Rule of 72 in action
£10,000 lump sum · 7.2% rate · 10 years · no monthly contributions · monthly compounding
£20,000 lump sum · 6.0% rate · 15 years · no monthly contributions · monthly compounding
Total contributed£20,000
Interest earned£29,082
Final balance£49,082
James's example demonstrates the Rule of 72: at 7.2%, a lump sum roughly doubles in 10 years. The final balance of £20,500 slightly exceeds doubling because monthly compounding is more frequent than annual. All projections assume the stated rate is maintained for the full period. Not financial advice.
Frequently Asked Questions
With simple interest, you earn interest only on your original principal — £10,000 at 5% earns exactly £500 every year. Over 10 years that is £5,000 in interest and a final balance of £15,000. With compound interest, every interest payment is added to the balance and earns interest in future periods. At 5% compounded annually, £10,000 grows to £16,289 over 10 years — £1,289 more than simple interest, purely because past interest earned more interest. Over longer periods and at higher rates, compound interest produces dramatically larger balances: at 5% over 40 years, the compound advantage over simple interest exceeds £50,000 on a £10,000 deposit.
At typical UK savings rates (4–5%), the difference between daily and annual compounding is surprisingly small. On £10,000 at 5% over 10 years: annually produces £16,289; monthly produces £16,470; daily produces £16,487. The difference between annual and daily compounding is just £198. The gap grows at higher rates and over longer periods, but for UK savings purposes it is largely academic because accounts quote AER — which already standardises for frequency. If two accounts have the same AER, they will produce identical balances regardless of how frequently interest is technically calculated.
The Rule of 72 is a mental shortcut: divide 72 by the annual interest rate to estimate the number of years for a lump sum to double. At 6% it takes roughly 12 years (72 ÷ 6). At 8% it takes 9 years. At 4% it takes 18 years. The rule is an approximation that works best for rates between 4% and 15% with annual compounding. With monthly compounding you double slightly faster, as James's example above shows (7.2% monthly compounding over 10 years produces £20,500 — slightly more than double, beating the rule's prediction). For higher rates the rule overestimates time to double — at 15%, 72÷15 = 4.8 years, but the actual answer is about 4.7 years.
AER stands for Annual Equivalent Rate. It expresses a savings rate as if interest were compounded once per year, making it easy to compare accounts regardless of how often they actually compound. A savings account paying 0.40% per month has a monthly rate of 0.40% but an AER of (1.004)¹² − 1 = 4.91% — noticeably higher than 0.40% × 12 = 4.80%. UK law (the Consumer Credit Act and FCA rules) requires all savings providers to display AER alongside any quoted rate. When using this calculator, always enter the AER figure shown on your account rather than a nominal or gross rate — this gives you the most accurate projection regardless of the account's actual compounding frequency.