Compound Interest Calculator

About Compound Interest Calculator

The Compound Interest Formula

Without contributions, the formula is:

A = P(1 + r/n)^(nt)

Where A is the final amount, P is the principal (starting balance), r is the annual interest rate (as a decimal), n is the number of times interest compounds per year, and t is the number of years.

Worked example: £10,000 at 5% annual interest, compounded monthly, for 10 years:

A = 10000 x (1 + 0.05/12)^(12 x 10) = 10000 x (1.004167)^120 = 10000 x 1.6470 = £16,470.09

You earned £6,470.09 in interest without adding a penny. The same £10,000 at simple interest would only earn £5,000 (£500 per year for 10 years). That extra £1,470 is the interest earned on interest.

How Compounding Frequency Affects Returns

More frequent compounding means interest gets added to the balance sooner, which then earns its own interest. Here is £10,000 at 6% for 10 years with different frequencies:

Frequency	Times Per Year	Final Balance	Total Interest
Annually	1	£17,908.48	£7,908.48
Quarterly	4	£18,140.18	£8,140.18
Monthly	12	£18,193.97	£8,193.97
Daily	365	£18,220.44	£8,220.44

Monthly vs annual compounding makes a £285 difference over 10 years at 6%. The gap between monthly and daily is only about £26. Most savings accounts compound daily or monthly. The difference between those two is negligible for practical purposes.

The Power of Regular Contributions

Regular monthly deposits have an outsized effect because each one starts compounding immediately. Compare two strategies for reaching a goal over 20 years at 7% annual return:

Strategy	Starting Amount	Monthly Deposit	Total Contributed	Final Balance	Interest Earned
Lump sum only	£20,000	£0	£20,000	£77,394	£57,394
Monthly only	£0	£200	£48,000	£104,185	£56,185
Both	£20,000	£200	£68,000	£181,579	£113,579

The monthly-only strategy contributes £28,000 more cash but ends up with £27,000 more total value. The combined approach benefits from both the lump sum compounding for the full 20 years and each monthly deposit compounding from its own start date.

The Rule of 72

A quick way to estimate doubling time: divide 72 by the annual interest rate.

Interest Rate	Doubling Time (Rule of 72)	Actual Doubling Time
2%	36 years	35.0 years
4%	18 years	17.7 years
6%	12 years	11.9 years
8%	9 years	9.0 years
10%	7.2 years	7.3 years
12%	6 years	6.1 years

The Rule of 72 calculator gives you exact figures for any rate.

Compound Interest vs Compound Growth

The compound interest formula applies to more than just bank accounts. Stock market returns, property appreciation, inflation, and even population growth all follow compound growth patterns.

• Savings accounts: As of April 2026, top UK easy-access accounts pay up to 4.75% AER, though the average easy-access rate has dipped to around 2.4% following Bank of England base rate cuts to 3.75%, according to Moneyfacts. In the US, top high-yield savings accounts offer up to 5.00% APY, while the FDIC national average sits at just 0.39%, according to Bankrate data from April 2026.
• Stock market: The S&P 500 has returned an average of 10.4% annually since 1926 (about 7.2% after inflation), according to historical data compiled by NYU Stern. The index returned 17.9% in 2025, following 25.0% in 2024 and 26.3% in 2023. Individual years vary wildly - the S&P 500 only landed within 2 percentage points of its 10% average in 6 of the past 93 years - but compound growth explains why long-term investing works.
• ISAs: In the UK, ISA interest is tax-free, so the compound interest formula gives you the exact take-home amount. Use the ISA calculator to model this specifically.
• Debt: Compound interest works against you on loans and credit cards. A credit card balance at 20% APR compounded monthly grows much faster than a savings account at 5%. Paying down high-interest debt is effectively an investment at that debt's interest rate.

The Cost of Waiting

Starting early matters enormously because of compounding. Consider two people who each invest £200/month at 7% annual return:

• Person A starts at age 25 and stops at 35 (10 years, £24,000 contributed)
• Person B starts at age 35 and continues to 65 (30 years, £72,000 contributed)

At age 65: Person A has about £354,000. Person B has about £243,000. Person A contributed £48,000 less but ended up with £111,000 more, purely because those early contributions had 30 extra years to compound.

Compound Interest and Inflation

Inflation erodes purchasing power at a compound rate too. If inflation averages 3% per year, prices roughly double every 24 years (72 / 3). To maintain real purchasing power, your investments need to earn above the inflation rate. A "real return" is the nominal return minus inflation. At 7% nominal growth and 3% inflation, the real return is roughly 4%.

For specific savings targets, the savings goal calculator tells you how much to deposit monthly. To measure returns on past investments, the ROI calculator computes total and annualised returns.

Compound Interest Working Against You: Credit Card Debt

Compounding is not always your friend. Credit cards charge compound interest on unpaid balances, and the rates are brutal. The average US credit card APR for all accounts was 21.00% in Q1 2026 (21.52% for accounts actually accruing interest), according to the Federal Reserve's G.19 consumer credit report released April 2026. UK credit cards averaged approximately 36% APR according to NimbleFins/Moneyfacts 2026 data.

Worked example: You carry a £3,000 balance at 22% APR, compounded daily, and only make the minimum payment (typically 2% of the balance or £25, whichever is higher):

• Month 1 payment: £60 (2% of £3,000). Of that, about £54 goes to interest and just £6 reduces the balance.
• After 12 months of minimum payments, you have paid £648 but still owe roughly £2,680.
• At this pace, it takes over 18 years to clear the balance and you pay about £3,800 in total interest on top of the original £3,000.

This is why paying more than the minimum is so important. Bumping that payment to £150/month clears the same debt in about 24 months and costs roughly £600 in interest instead of £3,800. The credit card payoff calculator shows exactly how different payment amounts affect your payoff timeline.

Historical Compound Growth: How Different Assets Stack Up

Different asset classes compound at very different rates. Here is how $10,000 invested in January 2004 would have grown by the end of 2024, based on historical index data compiled by NYU Stern and Federal Reserve Economic Data (FRED):

Asset Class	Avg Annual Return	$10,000 Becomes	Total Growth
S&P 500 (with dividends reinvested)	10.3%	$72,400	624%
US Aggregate Bonds (Bloomberg Index)	3.4%	$19,500	95%
US High-Yield Savings (average)	1.8%	$14,300	43%
Gold (spot price)	9.5%	$62,000	520%
US Inflation (CPI)	2.8%	$17,400	74%

The S&P 500 turned $10,000 into over $72,000, while a savings account barely kept pace with inflation. Bonds did beat inflation but only by a narrow margin. This is the core argument for investing rather than saving for long-term goals. That said, the S&P had terrible individual years mixed in (down 37% in 2008, down 18% in 2022), so this only works if you stay invested through the downturns.

Tax Wrappers and Compound Interest

Tax takes a bite out of compounding unless you use a tax-sheltered account. The exact impact depends on where you live and which wrapper you use:

Account Type	Country	Tax Treatment	Annual Limit (2026)
ISA (Cash or Stocks & Shares)	UK	Interest, dividends, and capital gains all tax-free	£20,000
Lifetime ISA (LISA)	UK	Tax-free + 25% government bonus on contributions	£4,000
401(k)	US	Tax-deferred: no tax on contributions or growth until withdrawal	$24,500 ($32,500 if 50+; $35,750 ages 60-63)
Roth IRA	US	Post-tax contributions, but all growth and withdrawals are tax-free	$7,500 ($8,600 if 50+)
SIPP/Pension	UK	Tax relief on contributions (20-45%), tax-deferred growth	100% of earnings

The difference is significant over decades. If you earn 7% annually in a taxable account and pay 20% tax on gains each year, your effective growth rate drops to about 5.6%. Over 30 years, £10,000 at 7% tax-free grows to £76,123. The same amount at 5.6% effective rate grows to only £51,269. That is roughly £25,000 lost to tax drag on a single £10,000 investment. Use the Roth IRA calculator to model US tax-free growth specifically.

Continuous vs Discrete Compounding

Most real-world accounts compound at fixed intervals (daily, monthly, annually). But the mathematical limit of infinitely frequent compounding is called continuous compounding, and it uses a different formula:

A = P x e^(rt)

Where e is Euler's number (approximately 2.71828), r is the annual rate, and t is years.

Comparison for £10,000 at 6% for 10 years:

Compounding	Final Balance	Difference from Annual
Annual	£17,908.48	-
Monthly	£18,193.97	+£285.49
Daily	£18,220.44	+£311.96
Continuous	£18,221.19	+£312.71

Continuous compounding gives only £0.75 more than daily compounding. In practice, the difference between daily and continuous is negligible. Continuous compounding mainly matters in mathematical finance and options pricing (it is the basis of the Black-Scholes model), not in everyday savings.

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Sources

• Federal Reserve - G.19 Consumer Credit Release
• NYU Stern - Historical Returns on Stocks, Bonds and Bills
• Moneyfacts - UK Easy Access Savings Rates
• Bank of England - Bank Rate
• Bankrate - US Savings Rates and FDIC National Averages
• GOV.UK - Individual Savings Accounts (ISAs)
• Federal Reserve Economic Data (FRED)