How do I calculate compound interest?

To calculate compound interest: (1) Convert the annual rate to a decimal (e.g., 5% = 0.05). (2) Divide by the compounding frequency n (e.g., 12 for monthly). (3) Multiply the time in years by n. (4) Apply the formula A = P(1 + r/n)^(nt). The compound interest earned is A − P.

How often should interest be compounded?

More frequent compounding produces slightly higher returns. For the same rate: annually < semi-annually < quarterly < monthly < daily < continuously. However, the difference between daily and continuous compounding is negligible. Most savings accounts compound daily, while many investments compound monthly or quarterly.

CAGR (Compound Annual Growth Rate) is the constant annual rate at which an investment would have grown from its beginning value to its ending value over a given period. Formula: CAGR = (FV/PV)^(1/t) − 1. It smooths out volatility and is useful for comparing investments with different time horizons.

How does the Rule of 72 work?

The Rule of 72 is a quick estimation: divide 72 by the annual interest rate to find roughly how many years it takes to double your money. At 6% interest: 72 ÷ 6 = 12 years to double. At 8%: 72 ÷ 8 = 9 years. At 12%: 72 ÷ 12 = 6 years. This rule works best for rates between 4% and 15%.

How do regular contributions affect compound interest?

Regular contributions dramatically accelerate growth because each contribution immediately begins earning compound interest. For example, $10,000 at 7% for 30 years grows to about $76,123. But adding just $200/month brings the total to approximately $317,000 — over 4× more. Consistency matters more than the initial amount.

What interest rate do I need to double my money in 10 years?

Using the Rule of 72: 72 ÷ 10 = 7.2% annual rate. More precisely, using the compound interest formula: rate = (2)^(1/10) − 1 ≈ 7.18% per year with annual compounding. This means you need roughly 7.2% annual return to double your investment in a decade.

Compound Interest Calculator

Calculate compound interest with daily, monthly, quarterly, or continuous compounding. Add regular contributions, visualize growth over time, and understand every formula. Educational tool — not financial advice.

✓ Free instant calculator ✓ All compounding frequencies ✓ Growth visualization ✓ Contributions supported ✓ Educational use

Compound Interest Calculator

Initial Principal (P)

Annual Interest Rate (r)

Time Period

Compounding Frequency (n)

Monthly Contribution (optional)

Annual Contribution (optional)

Results — Educational Estimate Only

Final Amount

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Total Interest Earned

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Principal—

Contributions—

Growth Multiple—

Composition Breakdown

Final Amount

Principal Contributions Interest

Growth Over Time

Compound Interest Formula

The compound interest formula calculates how money grows when interest is reinvested. There are two versions depending on the compounding type:

Standard Compound Interest Formula

A = P(1 + r/n)^(nt) Where: A = Final amount (principal + interest) P = Initial principal r = Annual interest rate (as a decimal, e.g., 5% = 0.05) n = Number of times interest compounds per year t = Number of years

Continuous Compound Interest Formula

A = P × e^(rt) Where: e = Euler's number ≈ 2.71828 All other variables are the same as above

Step-by-Step Example

Invest $10,000 at 7% annual rate, compounded monthly, for 10 years:

Identify variables: P = $10,000, r = 0.07, n = 12, t = 10
Calculate rate per period: r/n = 0.07/12 = 0.005833
Calculate total periods: nt = 12 × 10 = 120
Apply formula: A = $10,000 × (1.005833)^120
Result: A = $10,000 × 2.00966 = $20,096.61
Interest earned: $20,096.61 − $10,000 = $10,096.61

💡 Key insight: Your money more than doubled in 10 years at 7% — and you earned $10,097 in interest on a $10,000 investment. That's the power of compound growth.

Compound Interest with Regular Contributions

When you make regular contributions, the formula extends to include a future value of annuity component:

A = P(1 + r/n)^(nt) + PMT × [((1 + r/n)^(nt) − 1) / (r/n)] Where PMT = regular contribution amount per compounding period

Regular contributions dramatically accelerate wealth building because each new deposit immediately begins earning compound interest. Even small monthly additions create enormous differences over decades.

How Compound Interest Works

Compound interest is fundamentally different from simple interest because it creates exponential growth. Here's a year-by-year breakdown showing how $10,000 at 7% compounds annually:

Year	Starting Balance	Interest (7%)	Ending Balance
1	$10,000.00	$700.00	$10,700.00
2	$10,700.00	$749.00	$11,449.00
3	$11,449.00	$801.43	$12,250.43
5	$13,107.96	$917.56	$14,025.52
10	$18,384.59	$1,286.92	$19,671.51
20	$36,165.89	$2,531.61	$38,697.50
30	$71,142.57	$4,979.98	$76,122.55

Notice how the interest earned each year keeps increasing. By year 30, you're earning $4,980/year in interest — nearly half your original principal — each year. That's compound interest working for you.

Compounding Frequency Comparison

How does compounding frequency affect your returns? Here's $10,000 at 7% for 10 years with different frequencies:

Frequency	n	Final Amount	Interest Earned	Effective Rate
Annually	1	$19,671.51	$9,671.51	7.000%
Semi-Annually	2	$19,897.89	$9,897.89	7.123%
Quarterly	4	$20,015.97	$10,015.97	7.186%
Monthly	12	$20,096.61	$10,096.61	7.229%
Weekly	52	$20,118.78	$10,118.78	7.246%
Daily	365	$20,137.53	$10,137.53	7.250%
Continuous	∞	$20,137.53	$10,137.53	7.251%

💡 Takeaway: Moving from annual to monthly compounding adds ~$425 (a meaningful difference). But moving from daily to continuous adds less than $1. For most practical purposes, daily and continuous compounding are essentially identical.

Compound Interest vs Simple Interest

📈 Compound Interest

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

Interest earned on principal AND accumulated interest
Grows exponentially over time
Used by: savings accounts, CDs, investments, loans
$10,000 at 7% for 30 years = $76,123

📊 Simple Interest

Formula: I = P × r × t

Interest earned only on the original principal
Grows linearly (straight line)
Used by: some bonds, car loans, short-term loans
$10,000 at 7% for 30 years = $31,000

⚠ The difference is massive: Over 30 years, compound interest produces $76,123 vs simple interest at $31,000 — that's 2.5× more money from the same rate and principal. Time is the most powerful ingredient in compounding.

CAGR — Compound Annual Growth Rate

The Compound Annual Growth Rate (CAGR) tells you the constant annual rate at which an investment would have grown from its beginning value to its ending value. It smooths out year-to-year volatility.

CAGR = (Final Value / Initial Value)^(1/t) − 1 Example: $10,000 grows to $25,000 in 8 years CAGR = (25000 / 10000)^(1/8) − 1 = (2.5)^(0.125) − 1 ≈ 0.1214 = 12.14%

CAGR is widely used in finance to compare investments, evaluate portfolio performance, and project future growth. It differs from average annual return because it accounts for compounding.

💡 Rule of 72: A quick shortcut — divide 72 by the annual interest rate to estimate how many years it takes to double your money. At 6%: 72 ÷ 6 = 12 years. At 8%: 72 ÷ 8 = 9 years. At 12%: 72 ÷ 12 = 6 years.

Daily Compound Interest — How It Works

Daily compounding means interest is calculated and added to your balance every single day. With n = 365, the formula becomes:

A = P(1 + r/365)^(365 × t)

Most high-yield savings accounts, money market accounts, and many certificates of deposit (CDs) use daily compounding. Here's why it matters:

💰 Daily vs Monthly: $50,000 at 5% for 20 years

Monthly Compounding (n=12)$135,632.44

Daily Compounding (n=365)$135,914.07

Extra from Daily Compounding$281.63

The difference is small but real. Over very large balances or very long time periods, daily compounding provides a consistent edge.

Continuous Compound Interest Explained

Continuous compounding is the mathematical limit of compounding frequency — interest is compounded an infinite number of times per year. The formula uses Euler's number (e ≈ 2.71828):

A = P × e^(rt) Interest = P × e^(rt) − P = P(e^(rt) − 1)

While no real-world bank compounds continuously, this formula is important in:

Financial mathematics: Pricing derivatives, options, and bonds
Academic finance: Theoretical models and proofs
Upper bound estimation: Maximum possible return for a given rate
Natural growth: Population growth, radioactive decay, and other natural phenomena

🔬 Continuous vs Daily: $10,000 at 7% for 10 years

Daily Compounding$20,137.53

Continuous Compounding$20,137.53

Difference < $0.01

💡 Practical takeaway: The difference between daily and continuous compounding is negligible (often less than a penny). Continuous compounding is primarily a theoretical concept. Focus on the interest rate and time — those are the real drivers of growth.

Compound Interest Examples

📊 Example 1: College Fund — $5,000 for 18 years at 6%

Principal$5,000

Monthly Contribution$100

Rate / Compounding6% / Monthly

Time18 years

Final Amount$53,448

Total Contributions$26,600

Interest Earned$26,848

📊 Example 2: Retirement — $25,000 for 30 years at 8%

Principal$25,000

Monthly Contribution$500

Rate / Compounding8% / Monthly

Time30 years

Final Amount$976,479

Total Contributions$205,000

Interest Earned$771,479

📊 Example 3: Short-term Savings — $1,000 at 5% daily for 5 years

Principal$1,000

Monthly Contribution$0

Rate / Compounding5% / Daily

Time5 years

Final Amount$1,284.03

Interest Earned$284.03

📊 Example 4: The Power of Starting Early

Person A: starts at 25, invests $200/mo for 40 years at 7%$527,587

Person B: starts at 35, invests $200/mo for 30 years at 7%$243,994

Person A contributed only $24,000 more but earned...$283,593 more

Frequently Asked Questions About Compound Interest

What is compound interest?

Compound interest is interest calculated on both the initial principal and the accumulated interest from all previous periods. Unlike simple interest, which only grows linearly, compound interest grows exponentially — you earn "interest on your interest." This accelerating effect becomes more dramatic over longer time periods.

What is the compound interest formula?

The standard formula is A = P(1 + r/n)^(nt), where A is the final amount, P is principal, r is the annual rate as a decimal, n is compounding frequency per year, and t is time in years. For continuous compounding: A = Pe^(rt). Enter your values above for an instant calculation.

How do I compute compound interest?

Step 1: Convert the annual rate to decimal (e.g., 7% → 0.07). Step 2: Divide by compounding frequency n. Step 3: Multiply years by n to get total periods. Step 4: Apply A = P(1 + r/n)^(nt). Step 5: Subtract P to find the interest portion. Or simply enter your values in the calculator above.

What's the difference between compound and simple interest?

Simple interest = P × r × t (linear growth on principal only). Compound interest = P(1 + r/n)^(nt) (exponential growth on principal + accumulated interest). Example: $10,000 at 7% for 30 years → simple interest yields $31,000 while compound interest yields $76,123 — almost 2.5× more.

How often should interest compound?

More frequent compounding yields slightly higher returns: annually < quarterly < monthly < daily < continuous. However, the gains diminish rapidly. The jump from annual to monthly compounding is meaningful; from daily to continuous is negligible. Most savings accounts compound daily.

What is daily compound interest?

Daily compounding calculates and adds interest every day (n = 365). The formula becomes A = P(1 + r/365)^(365t). Most high-yield savings accounts and CDs use daily compounding. It yields slightly more than monthly compounding but the difference is typically small.

What is continuous compounding?

Continuous compounding compounds interest infinitely often. The formula is A = Pe^(rt), where e ≈ 2.71828. It represents the mathematical upper limit of compounding. In practice, it produces almost identical results to daily compounding and is primarily used in financial theory and derivatives pricing.

What is the Rule of 72?

The Rule of 72 provides a quick estimate: divide 72 by the annual rate to find how many years it takes to double your money. At 6%: 72 ÷ 6 = 12 years. At 9%: 72 ÷ 9 = 8 years. It works best for rates between 4% and 15% and assumes annual compounding.

What is CAGR?

CAGR (Compound Annual Growth Rate) is the constant annual rate that would take an investment from its initial value to its final value over a given period. Formula: CAGR = (FV/PV)^(1/t) − 1. It's useful for comparing investments because it smooths out year-to-year volatility.

How do contributions affect compound interest?

Regular contributions massively amplify compound interest. $10,000 at 7% for 30 years grows to about $76,123 alone. Adding $200/month brings the total to approximately $317,000 — over 4× more. Each contribution begins compounding immediately, creating a snowball effect.

Is compound interest good or bad?

It works both ways. When saving and investing, compound interest accelerates your wealth exponentially — it's your greatest ally. When borrowing (especially credit cards at 15–25% APR), compound interest works against you and can make debt spiral quickly. The key is to earn it, not owe it.

How much will $10,000 grow in 20 years?

At 7% compounded monthly: $10,000 grows to approximately $40,387 — quadrupling your money. At 5%: about $27,126. At 10%: about $73,281. The rate makes an enormous difference over 20 years. Add $200/month at 7% and you'd reach roughly $144,786.

Related Calculators

Disclaimer: This Compound Interest Calculator is for educational and informational purposes only. Results are estimates based on constant rates and regular contributions — actual returns will vary. This tool does not constitute financial, investment, or tax advice. Consult a qualified financial advisor before making investment decisions.