What is compound interest and how is it different from simple interest?

Simple interest is calculated only on the original principal — £10,000 at 5% earns £500 every year, totalling £5,000 over 10 years. Compound interest is calculated on the principal plus all previously accumulated interest — so the interest itself earns interest. At 5% compounded annually, £10,000 grows to £16,289 over 10 years — £1,289 more than simple interest. Over longer periods and at higher rates, the difference becomes dramatically larger. This is why compound interest is often described as exponential rather than linear growth.

Does compound frequency make a significant difference?

For typical UK savings rates, the difference between daily and annual compounding is smaller than many expect. On £10,000 at 5% over 10 years: annual compounding produces £16,289, while daily compounding produces £16,487 — a difference of just £198. The impact becomes more noticeable with higher rates or longer periods. UK savings accounts quote rates as AER (Annual Equivalent Rate), which already accounts for the effect of compounding frequency — two accounts with identical AERs will grow at the same rate regardless of how often they technically compound.

What is the Rule of 72?

The Rule of 72 is a quick mental calculation for estimating how long it takes to double your money at a fixed interest rate. Simply divide 72 by the annual interest rate: at 6% it takes roughly 72÷6 = 12 years to double. At 8% it takes 9 years. At 4% it takes 18 years. The rule is an approximation — it works best for rates between 4% and 15% and assumes annual compounding. More frequent compounding (monthly or daily) will cause the money to double slightly faster than the rule predicts.

What is AER and how does it relate to compound interest?

AER stands for Annual Equivalent Rate. It is the standardised rate that shows what a savings account's interest rate is equivalent to if interest were compounded annually. For example, a savings account paying 0.4% per month has a nominal monthly rate of 0.4% but an AER of (1.004)¹² − 1 = 4.91%. UK providers are legally required to display AER alongside any quoted rate, making it straightforward to compare accounts on a like-for-like basis. When using this calculator, enter the AER shown on your account to get the most accurate projection.

Compound Interest Calculator 2026 — Daily, Monthly & Annual

Calculate Compound Growth

Initial Deposit

Starting amount (leave at 0 if saving from scratch)

Monthly Contribution

Optional: regular amount added each month

Annual Interest Rate

Enter the AER shown on your account for accuracy

Time Period

yrs

Compound Frequency How often interest is calculated and added to your balance

Contributions Interest earned

Initial deposit	—
Monthly contributions	—
Total contributed	—
Compound frequency	—
Annual interest rate	—
Time period	—
Total interest earned	—

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%:

≈ 24 years

≈ 18 years

≈ 14.4 years

≈ 12 years

7.2%

≈ 10 years

≈ 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

Total contributed£10,000

Interest earned£10,500

Final balance£20,500

Sarah, 25 — Regular saver

£0 initial · £250/month · 5.0% rate · 20 years · monthly compounding

Total contributed£60,000

Interest earned£42,758

Final balance£102,758

Emma, 45 — Lump sum investment

£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.

Compound Interest Calculator 2026

Calculate Compound Growth

How your result compares across compound frequencies

How Compound Interest Works

Simple Interest vs Compound Interest

The Compound Interest Formula

The Rule of 72 — Doubling Your Money

Does Compound Frequency Really Matter?

The Most Powerful Variable: Time

What Is AER?

Worked Examples

Frequently Asked Questions

Related Calculators

Rates, assumptions and sources