What is the compound interest formula?

The formula is A = P(1 + r/n)^(nt), where P is principal, r is annual rate, n is compounding frequency per year, and t is time in years.

How often should interest compound for maximum growth?

More frequent compounding always yields more. Daily compounding yields slightly more than monthly, which yields more than annual compounding.

What is the Rule of 72?

Divide 72 by your annual interest rate to estimate how many years it takes to double your money. At 8% it takes approximately 9 years.

Finance Calculator

See how $10,000 grows to $46,610 — and exactly how to beat it

Q: What is compound interest?

Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. Unlike simple interest, it grows exponentially over time.

Adjust any value and watch results update instantly. Compare two scenarios side-by-side, export a full PDF report, or share a link with your exact figures.

💡At 8%, your money doubles every ~9.0 years (Rule of 72)

Used by 50,000+ users monthly · No sign-up required · Instant results

Final balance

$21,589

After 10 years

Interest earned

$11,589

115.9% return

Total invested

$10,000

Principal + contributions

Used by 50,000+ users monthly · No sign-up required · Instant results

Compound vs. simple interest

Compound

$21,589

Simple

$18,000

Bonus

+$3,589

Scenario comparisonNew

Scenario A

Principal ($)

Rate (%)

Years

Monthly ($)

$21,589

Final balance

Scenario B★ Winner

Principal ($)

Rate (%)

Years

Monthly ($)

$25,937

Final balance

+$4,348Scenario B earns $4,348 more — that's 20.1% better over 10 years

Growth over time

Compound balance

Simple interest

💡

Boost your outcome

Adding just $50/month more in contributions would grow your balance by an extra $9,208 over 10 years.

⏱

Rule of 72

9.0 yrs

Time to double your money at this rate

📈

Effective rate

8.00%

True annual return after compounding

💰

Monthly interest

$133

Avg. interest earned per month in final year

🎯

10× milestone

29.9 yrs

Years to 10× your investment at this rate

The compound interest formula

A = P(1 + r/n)nt

AFinal amount

PPrincipal (initial investment)

rAnnual interest rate (decimal)

nCompounding periods per year

tTime in years

Worked example

You invest $10,000 at 8% per year, compounded monthly, for 10 years:

A = 10,000 × (1 + 0.08/12)^(12×10)
A = 10,000 × (1.00667)^120
A = $22,196

Of the $22,196 final balance, $10,000 is your principal. The remaining $12,196 is pure compound interest — earned without any additional deposits.

How compound interest works

Compound interest is often called the “eighth wonder of the world”. Unlike simple interest — which only applies to your original principal — compound interest calculates interest on both your principal and all previously earned interest. Each period, your interest earns its own interest, creating exponential rather than linear growth.

The difference is dramatic over time. At 8% simple interest, $10,000 grows to $18,000 after 10 years. At 8% compound interest (monthly), it grows to $22,196 — $4,196 more for doing nothing differently.

Why starting early matters more than amount

Consider two investors both earning 7% per year. Investor A invests $500/month from age 25–35 then stops (total invested: $60,000). Investor B invests $500/month from age 35–65 (total invested: $180,000). At age 65, Investor A has approximately $602,000 — more than Investor B's $567,000, despite investing a third as much. Time is the most powerful variable.

Works against you on debt

The same mathematics that builds wealth also accelerates debt. A $5,000 credit card balance at 20% interest with minimum payments only takes over 30 years to repay and costs $13,000+ in interest. Understanding compound interest on both sides of the equation is essential for financial decision-making.

How compounding frequency affects your returns

The more frequently interest compounds, the higher your effective annual return. For $10,000 at 8% for 10 years, here's what each compounding frequency produces:

Frequency	Times/year (n)	Final balance	Interest earned	Effective rate
Annually	1	$21,589	$11,589	8.00%
Semi-annually	2	$21,911	$11,911	8.16%
Quarterly	4	$22,080	$12,080	8.24%
Monthly	12	$22,196	$12,196	8.30%
Daily	365	$22,253	$12,253	8.33%

Notice that going from annual to daily compounding only adds $664 — compounding frequency matters far less than the interest rate and time horizon. Use the Rule of 72 to estimate doubling time mentally: divide 72 by your rate. At 8%, money doubles every 9 years.

The impact of regular contributions

Adding a regular monthly contribution dramatically accelerates growth. Toggle the Monthly contributions switch in the calculator above to model this. Here's a comparison of $10,000 lump sum vs $200/month added, both at 8% for 20 years:

Lump sum only ($10,000)

$46,610

Invested: $10,000 · Interest: $36,610

Lump sum + $200/month

$164,743

Invested: $58,000 · Interest: $106,743

Adding just $200/month increases the final balance by over $118,000. Regular contributions are the most practical way most investors build wealth — the mathematical force of compound interest handles the rest. See how this applies to Australian superannuation in our super guide.

Frequently asked questions

Compound interest is interest calculated on both your initial principal and the accumulated interest from previous periods. Unlike simple interest — which only applies to your original deposit — compound interest snowballs over time because each interest payment is added to your balance and then earns interest itself. This "interest on interest" effect is why Albert Einstein reportedly called compound interest the eighth wonder of the world. The longer your money compounds, the more dramatic the effect becomes. A $10,000 investment at 8% simple interest earns $800 per year, every year. The same investment with compound interest earns $800 in year one, but $864 in year two, $933 in year three — and so on, accelerating indefinitely. The key variables are your principal, interest rate, compounding frequency, and time. Of these, time is often the most powerful. Starting 10 years earlier can more than double your final balance, even at the same rate.

The compound interest 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 expressed as a decimal, n is the number of times interest compounds per year, and t is the number of years. For example, to calculate compound interest on $10,000 at 8% annual rate, compounded annually for 10 years: A = 10,000 × (1 + 0.08/1)^(1×10) = 10,000 × (1.08)^10 = $21,589. That means $11,589 in interest earned on a $10,000 investment — a 115.9% return. With monthly compounding at the same rate: A = 10,000 × (1 + 0.08/12)^(12×10) = $22,196. The more frequently interest compounds, the higher the effective annual rate. This difference becomes substantial over 20–30 year timeframes, which is why understanding compounding frequency is essential when comparing savings accounts, investment products, or loans.

The more frequently interest compounds, the more you earn — but the incremental gains diminish as frequency increases. The jump from annual to monthly compounding is significant. Moving from monthly to daily is much smaller. Continuous compounding (theoretically infinite periods) only marginally outperforms daily. At 8% for 10 years on $10,000: annual compounding yields $21,589; monthly compounding yields $22,196; daily compounding yields $22,253. The difference between monthly and daily is only $57 — not worth stressing over. The difference between annual and monthly ($607) is more meaningful at scale. Most high-yield savings accounts and term deposits compound daily or monthly. Investment accounts and super funds typically compound annually or quarterly. Credit cards — where compounding works against you — often compound daily, which accelerates debt quickly. When comparing financial products, always check the effective annual rate (EAR), which accounts for compounding frequency and gives you a true apples-to-apples comparison.

The Rule of 72 is a simple mental shortcut for estimating how long it takes to double your money: divide 72 by your annual interest rate. At 6%, your money doubles in approximately 12 years (72 ÷ 6). At 9%, it doubles in 8 years (72 ÷ 9). At 12%, it doubles in just 6 years. The rule works because of the mathematical properties of exponential growth. It's accurate to within about 1% for rates between 6% and 10%, making it a reliable back-of-envelope tool. For rates outside this range, use 70 ÷ rate for lower rates or 74 ÷ rate for higher rates. The Rule of 72 also works in reverse: to find the rate needed to double in a given number of years, divide 72 by those years. To double your money in 8 years, you need roughly 9% annual return (72 ÷ 8). This insight calculator above shows you the exact doubling time for your current rate, updated in real time.

Yes — and this is one of the most important financial concepts to understand. Compound interest is mathematically identical whether it's working for you (savings and investments) or against you (debt). The same exponential growth that builds wealth on your savings destroys it on high-interest debt. A $5,000 credit card balance at 20% interest, with no payments, grows to over $30,000 in 10 years through compounding alone. Many credit cards compound daily, which accelerates this further. This is why financial advisors universally recommend paying off high-interest debt before investing — a guaranteed 20% return (by eliminating 20% interest) beats almost any investment return. The key difference between good debt (mortgage at 6%) and bad debt (credit card at 20%) is the interest rate relative to what your money could earn elsewhere. Our loan repayment calculator can show you exactly how much interest you'd save by making extra repayments.

The effective annual rate (EAR) — also called the annual equivalent rate (AER) in some countries — is the true annualised return after accounting for compounding within the year. It lets you compare financial products with different compounding frequencies on equal footing. The formula is: EAR = (1 + r/n)^n − 1, where r is the nominal rate and n is compounding periods per year. A nominal 8% compounded monthly has an EAR of (1 + 0.08/12)^12 − 1 = 8.30%. A nominal 8% compounded daily has an EAR of 8.33%. The EAR is always higher than the nominal rate (except with annual compounding, where they're equal). When banks advertise savings accounts, they're legally required in most countries to disclose the EAR (or APY in the US). When comparing investment returns, loans, or savings rates, always compare EARs — not nominal rates. A 7.9% nominal rate compounded daily actually beats an 8.0% nominal rate compounded annually. The insights panel in this calculator displays your exact EAR in real time.