Use our calculator to apply the compound interest formula and see how your money grows. Understand the impact of the compound interest rate formula with detailed projections and interactive charts.
Learn how compound interest accelerates your savings and investments through reinvested returns.
Begin with your initial deposit or investment amount.
Interest is added to both your original principal and previously earned interest, increasing your balance faster.
Over time, your earnings multiply as interest compounds on interest, boosting your long-term wealth.
Enter your values in the left panel and click Calculate Growth. The chart and four result cards update instantly.
The starting amount you invest or deposit today. For a savings account, this is your opening balance. For a retirement projection, enter your current account balance. Enter 0 if you are starting from scratch with contributions only.
Enter the expected annual rate as a percentage (e.g., 5 for 5%). For savings accounts, use the APY shown on the account. For investment projections, use the expected average annual return (commonly 6–10% for diversified stock portfolios historically). This is the nominal rate used in the A=P(1+r/n)^nt formula.
Choose how often interest compounds: Monthly is standard for savings accounts and CDs. Daily gives slightly higher results and is used by some banks. Annually is typical for bonds. Set Time Period in whole years (e.g., 10 for a 10-year projection).
Optional. Enter the amount you add each month. The calculator adds contributions monthly and compounds them alongside your principal. Even a small $50/month contribution compounds substantially over decades. Leave at $0 for a pure lump-sum projection.
The projected total balance at the end of your time period — principal + all contributions + all compound interest earned. This is what your account is projected to be worth if the rate stays constant.
The pure compound interest earned: Final Amount minus all money you actually put in. This grows faster in later years because interest compounds on an ever-larger base — the defining feature of exponential growth.
The total cash you contributed: starting principal plus all monthly contributions. Compare this to Final Amount to see how much of your wealth came from compound interest versus out-of-pocket deposits.
Total percentage gain: (Final Amount − Original Principal) ÷ Original Principal × 100. A 200% growth rate means your original principal tripled. This is the total ROI, not an annualized figure.
APR (Annual Percentage Rate) is the nominal stated rate before compounding. APY (Annual Percentage Yield) includes the effect of compounding and shows your actual yearly return.
APY = (1 + APR/n)^n − 1
Example: 5% APR monthly → APY = (1 + 0.05/12)^12 − 1 = 5.116%
When comparing savings accounts or CDs, always compare APY to APY. In this calculator, enter APR in the Rate field for formula-exact results; enter APY to match your bank statement return.
The compound interest formula has been the foundation of financial mathematics for centuries. Here are all the key formulas with worked examples.
Standard: A = P(1 + r/n)^(n×t)
Continuous: A = P × e^(r×t)
CAGR: CAGR = (Final / Initial)^(1/Years) − 1
Simple (comparison): A = P(1 + r×t)
Rate from end values: r = n × [(A/P)^(1/n×t) − 1]
Where: A = final amount, P = principal, r = annual rate (decimal), n = compounding periods per year, t = years, e ≈ 2.71828 (Euler’s number).
Scenario: You deposit $5,000 at 4.5% APR compounded monthly for 5 years, adding $200/month.
$10,000 at 5% for 10 years, no contributions.
| Frequency | n/year | Final Amount | Interest |
|---|---|---|---|
| Annually | 1 | $16,288.95 | $6,288.95 |
| Semi-annually | 2 | $16,386.16 | $6,386.16 |
| Quarterly | 4 | $16,436.19 | $6,436.19 |
| Monthly | 12 | $16,470.09 | $6,470.09 |
| Daily | 365 | $16,486.65 | $6,486.65 |
| Continuous | ∞ | $16,487.21 | $6,487.21 |
Monthly earns $181 more than annual on $10,000. Diminishing returns set in quickly beyond monthly.
| Year | Simple Interest | Compound Interest | Advantage |
|---|---|---|---|
| 5 | $13,500 | $14,026 | +$526 |
| 10 | $17,000 | $19,672 | +$2,672 |
| 20 | $24,000 | $38,697 | +$14,697 |
| 30 | $31,000 | $76,123 | +$45,123 |
Enter your HYSA balance as Principal and your APY as Rate. Select Monthly compounding. Add your monthly auto-transfer as Monthly Contribution. A $10,000 balance at 4.5% APY + $300/month grows to approximately $37,000 in 5 years, with $2,700 in interest on top of $28,000 contributed.
CDs lock in a fixed rate for a defined term. Enter the CD rate (e.g., 4.8%) and select the compounding frequency (monthly or daily). Leave Monthly Contribution at $0. A $15,000 CD at 4.8% for 2 years compounded monthly → $16,492 final value, with $1,492 in interest.
Enter your current balance as Principal. Use 6–8% for a diversified portfolio. Enter your monthly contribution. Example: $25,000 + $500/month at 7% for 25 years → approximately $530,000. The 2025 401(k) limit is $23,500/year ($31,000 if age 50+).
Use 5–6% as a conservative return. A $3,000 start + $150/month at 6% for 16 years → approximately $58,000 projected. Compare this to current 4-year college costs (averaging $110,000+ at public universities) to plan your monthly contribution target.
Run the calculator twice with different rates. $20,000 in a HYSA at 4.5% vs. invested at 7% for 10 years: HYSA → $31,188. Index fund → $39,343. The $8,155 difference is the opportunity cost of keeping excess cash in savings instead of investing.
Enter credit card balance as Principal, APR as Rate, select Daily, Monthly Contribution = $0. See how fast the balance grows with no payments. A $5,000 balance at 24% APR for 5 years with no payments becomes $16,119 — a powerful illustration of why high-interest debt needs urgent attention.
Two of the most useful shortcuts in finance — plus how the same compound interest formula works against borrowers.
CAGR tells you the consistent annual rate of return that produced a given growth, smoothing out year-to-year volatility.
CAGR = (Final / Initial)^(1/Years) − 1
| Growth Scenario | CAGR |
|---|---|
| $10K → $18K in 6 years | 10.3% |
| $5K → $12K in 10 years | 9.1% |
| $20K → $30K in 5 years | 8.4% |
| S&P 500 (2014–2024 avg) | ~12.9% |
Divide 72 by the annual rate to estimate years to double your money.
| Rate | Years to Double | Example |
|---|---|---|
| 4% | 18 yrs | HYSA/CD (2025) |
| 6% | 12 yrs | Conservative fund |
| 8% | 9 yrs | Balanced portfolio |
| 10% | 7.2 yrs | Historical stock avg |
| 24% | 3 yrs | Credit card (against you) |
A $5,000 credit card balance at 24% APR compounded daily: with no payments, it grows to $6,360 after 1 year and $16,119 after 5 years. Debt doubles every 3 years at 24% (Rule of 72: 72 ÷ 24 = 3).
Unpaid student loan interest can “capitalize” — adding to principal when repayment begins. A $30,000 loan with $4,000 in accumulated interest becomes a $34,000 principal; you then pay interest on $34,000, not $30,000.
Enter your loan or credit card balance as Principal, the APR as Rate, select Daily or Monthly, and set Monthly Contribution to $0. The Final Amount shows how large the balance grows without payments — motivating urgency for debt repayment.
California state law (Civil Code 3289) limits compound interest on loans in some contexts, though credit cards under federal law (National Bank Act) are generally exempt. California bank CDs and savings accounts do compound interest daily or monthly per their terms. Always verify your APY before projecting growth.
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Common questions about compound interest, formulas, and financial growth
Compound interest earns on both your principal and previously accumulated interest. $10,000 at 7% annually: year 1 earns $700; year 2 earns $749 on $10,700. After 10 years: $19,672 vs $17,000 with simple interest. The longer the time horizon, the greater the compounding advantage.
A = P(1 + r/n)^(nt), where A = final amount, P = principal, r = annual rate (decimal), n = compounding periods/year, t = years. For $10,000 at 5% monthly for 3 years: A = 10,000 × (1 + 0.05/12)^36 = $11,614.72. For continuous compounding: A = Pe^(rt).
Simple: A = P(1+rt) — earned only on original principal. $10,000 at 7% for 10 years = $17,000. Compound earns on principal plus accumulated interest. Same scenario compounded annually = $19,672. At 30 years: $31,000 simple vs $76,123 compound — compound grows 2.5× more.
A = Pe^(rt) where e ≈ 2.71828. $10,000 at 5% for 10 years continuously = $16,487.21 vs $16,470.09 with monthly compounding — only $17 more. Diminishing returns set in quickly beyond daily compounding. Continuous compounding is used in advanced finance and theoretical pricing models.
CAGR (Compound Annual Growth Rate) = (Final/Initial)^(1/Years) − 1. It measures the consistent annual return that produced a given total growth. $10,000 growing to $18,000 in 6 years: CAGR = (1.8)^(1/6) − 1 = 10.3%/year. Useful for comparing investments with different time horizons.
Divide 72 by the annual compound interest rate to estimate years to double. At 6%: 12 years. At 9%: 8 years. At 4% HYSA: 18 years. At 24% credit card APR: debt doubles in only 3 years. This shortcut works for rates between 4% and 15% with reasonable accuracy.
APR is the nominal rate before compounding. APY includes compounding: APY = (1 + APR/n)^n − 1. A 5% APR compounded monthly has an APY of 5.116%. Banks advertise savings accounts by APY. Always compare APY to APY when evaluating accounts. In this calculator, enter APR for formula-exact results.
$10,000 at 5% for 10 years: annual = $16,289, quarterly = $16,436, monthly = $16,470, daily = $16,487. Monthly earns $181 more than annual. The benefit is real but diminishing beyond monthly — the difference between daily and monthly is only $17 over 10 years.
Yes. At 24% APR daily, a $5,000 credit card balance grows to $6,360 in 1 year and $16,119 in 5 years without payments. Debt doubles every 3 years at 24%. Model your debt: enter balance as Principal, APR as Rate, select Daily, Contribution = $0 to see how fast unpaid balances compound.
Monthly contributions compound alongside your principal. $10,000 at 7% for 20 years with no contributions = $38,697. Add $200/month and the final value jumps to approximately $152,000. The $48,000 in contributions generates about $65,300 in compound interest — nearly 1.4× the contributions themselves.