Finanzas

Simple vs Compound Interest Calculator

Compare simple interest (I = P·r·t) vs compound interest (A = P(1+r/n)^nt) side by side. See the exact dollar difference, a year-by-year growth table, and Rule of 72 tips.

🗓️ Updated June 2026 Reviewed by
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Data updated: · Source: Consumer Financial Protection Bureau — APR vs APY explained
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Compound Interest CalculatorCalculate compound interest with monthly contributions. See end balance, total interest earned, and a year-by-year breakdown using the A=P(1+r/n)^(nt) formula.Simple Interest Calculator (I = P × r × t)Enter principal, annual rate, and time (years, months, or days). Get total interest, final amount, and monthly/daily breakdowns. Includes worked example and simple vs. compound table.Compound Interest Calculator (long-term)Simulate how your investment grows with compound interest, monthly contributions, annual rate, and time horizon. Ideal for retirement planning and long-term…Loan Payment CalculatorCalculate monthly payment, total cost, interest, and APR for a personal or mortgage loan using the standard amortization formula. Rate, term, and principal…
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Simple interest and compound interest are the two ways money grows (or debt piles up), and the gap between them is the single most important concept in personal finance. Simple interest uses the linear formula I = P·r·t — you earn (or owe) the same fixed dollar amount each year on the original principal. Compound interest uses the exponential formula A = P(1 + r/n)^(n·t) — interest itself starts earning interest, so balances curve upward faster every year. Knowing which formula a financial product uses changes the math dramatically. Most auto loans, short-term personal loans, and US Treasury bills use simple interest. Credit cards compound daily (which is why a $5,000 balance at 24% APR balloons so quickly). High-yield savings accounts (HYSAs) like Marcus, Ally, and Capital One 360 compound daily and credit monthly. Certificates of Deposit (CDs) typically compound daily or monthly. 30-year fixed mortgages compound monthly via amortization. Albert Einstein reportedly called compound interest "the eighth wonder of the world — he who understands it, earns it; he who doesn't, pays it." This calculator lets you see that wonder (or warning) for any dollar amount, rate, and time horizon, including a year-by-year breakdown and the Rule of 72 shortcut for estimating doubling time.

When to use this calculator

  • Shop high-yield savings accounts (HYSA) vs CDs by comparing APY, compounding frequency, and projected balance after 1, 3, and 5 years before locking funds at Marcus, Ally, Discover, or your local credit union.
  • Estimate the true lifetime cost of a 30-year fixed mortgage by comparing simple-interest amortization (what most lenders quote) against a fully compounded scenario, so you understand how much interest you really pay the bank.
  • Simulate how credit card debt explodes under daily compounding at 22–29% APR, and decide whether to attack it with a 0% APR balance transfer, a personal loan, or the avalanche method.
  • Project retirement growth in a 401(k), Roth IRA, or taxable brokerage assuming the S&P 500's long-run nominal CAGR (~10%) and see how starting at age 25 vs 35 changes your nest egg at 65.
  • Compare a simple-interest auto loan from a credit union against a compound-interest home equity line of credit (HELOC) when financing a major purchase, so you pick the cheaper structure.
  • Teach students, kids, or financial-coaching clients the time-value-of-money principle with concrete dollar examples — the side-by-side year table is built for classroom whiteboarding.

Compounding Frequency Impact: $10,000 at 5% APR for 10 Years

FrequencyPeriods/year (n)Final balanceInterest earned
Simple interest—$15,000$5,000
Annual1$16,289$6,289
Semi-annual2$16,386$6,386
Quarterly4$16,436$6,436
Monthly12$16,470$6,470
Daily365$16,487$6,487
Continuous∞$16,487$6,487

Fuente: fórmulas A = P(1 + r/n)^(n·t) y A = P·e^(r·t); valores derivados de los datos de la calculadora. La diferencia entre capitalización mensual y diaria es de solo ~$17; comparar siempre por APY antes que por frecuencia.

How it works

Simple interest vs compound interest: the formulas

Simple interest is calculated only on the original principal. The amount you earn (or owe) each year never changes:

I = P × r × t
Final Balance = P + I

Where P is the principal in dollars, r is the annual rate as a decimal (7% → 0.07), and t is time in years.

Compound interest is calculated on the principal plus all previously earned interest. The interest base grows every period, so balances curve upward:

A = P × (1 + r/n)^(n × t)

Where n is the number of compounding periods per year (1 = annual, 12 = monthly, 365 = daily). For continuous compounding, the formula collapses to:

A = P × e^(r × t)

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Simple vs compound: dollar comparison at common rates

This table shows how $10,000 grows under simple interest vs monthly compounding at common saving rates:

RateTimeSimple totalCompound total (monthly)Difference
4%5 yr$12,000$12,210+$210
4%10 yr$14,000$14,908+$908
5%5 yr$12,500$12,834+$334
5%10 yr$15,000$16,470+$1,470
5%30 yr$25,000$44,677+$19,677
7%10 yr$17,000$20,097+$3,097
7%20 yr$24,000$40,388+$16,388
7%30 yr$31,000$81,165+$50,165
10%10 yr$20,000$27,070+$7,070
10%30 yr$40,000$198,374+$158,374

The compounding edge grows explosively with time. At 7% over 30 years, compound interest generates 5× more interest than simple interest on the same principal.

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Worked example: $10,000 at 7% for 10 years

Let's run the same $10,000 deposit at a 7% annual rate for 10 years under three different rules and see how the totals diverge.

Simple interest:

  • I = $10,000 × 0.07 × 10 = $7,000

  • Final balance = $10,000 + $7,000 = $17,000

    • Compound annually (n = 1):

  • A = $10,000 × (1 + 0.07/1)^(1 × 10)

  • A = $10,000 × 1.07^10 ≈ $10,000 × 1.9672

  • Final balance ≈ $19,672 (interest earned: $9,672)

    • Compound daily (n = 365):

  • A = $10,000 × (1 + 0.07/365)^(365 × 10)

  • A = $10,000 × 1.00019178^3650 ≈ $10,000 × 2.01375

  • Final balance ≈ $20,137 (interest earned: $10,137)

    • The $3,137 gap between simple and daily-compound over just 10 years is pure compounding effect — same principal, same rate, same time horizon.

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    Compounding frequency impact: daily vs monthly vs annual

    Using $10,000 at 5% APR for 10 years:

    FrequencynFinal balanceInterest earned
    Simple—$15,000$5,000
    Annual1$16,289$6,289
    Semi-annual2$16,386$6,386
    Quarterly4$16,436$6,436
    Monthly12$16,470$6,470
    Daily365$16,487$6,487
    Continuous∞$16,487$6,487

    The jump from annual to monthly adds ~$181. From monthly to daily, only ~$17. Shop for rate first, frequency second. A 4.50% HYSA compounded monthly will always beat a 4.30% HYSA compounded daily.

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    APR vs APY: what disclosure law actually requires

    APR (Annual Percentage Rate) is the nominal rate — quoted on credit cards, auto loans, and mortgages. The Truth in Lending Act (TILA, Regulation Z) requires lenders to disclose APR but it does not reflect compounding within the year. A 24.99% APR credit card actually charges closer to 28.18% effective.

    APY (Annual Percentage Yield) is the effective annual rate after compounding — quoted on HYSAs, CDs, and money market accounts. The Truth in Savings Act (Regulation DD) requires banks to disclose APY.

    The relationship:

    APY = (1 + APR/n)^n − 1

    Example: a 4.40% APY HYSA with daily compounding implies a nominal rate of ~4.31%. Always compare APYs when shopping savings products.

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    The Rule of 72 (and Rule of 114)

    The Rule of 72 estimates how many years it takes for money to double at a given annual compound rate:

    Years to double ≈ 72 / annual rate (%)

    RateYears to double
    4%18 years
    6%12 years
    8%9 years
    10% (S&P 500 avg)7.2 years
    24% (credit card)3 years
    36% (payday loan)2 years

    The Rule of 114 for tripling: Years to triple ≈ 114 / rate. The Rule of 144 for quadrupling. These rules are accurate within ~1% for rates between 4% and 12%.

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    Real-world examples

  • Marcus by Goldman Sachs HYSA at 4.40% APY: $10,000 → $12,408 after 5 years (daily compounding, monthly credit).

  • Ally CD 5-year at 4.00% APY: $10,000 → $12,167 at maturity.

  • S&P 500 historical CAGR (~10% nominal): $10,000 → $25,937 after 10 years assuming the long-run average; real returns vary wildly year-to-year.

  • 30-year fixed mortgage at 7.00%: $300,000 loan → ~$418,500 in total interest paid over 30 years.

  • Credit card balance at 24.99% APR: $5,000 minimum-payment-only → ~22 years to pay off and ~$10,400 in interest.

    • ---

    Continuous compounding: when does it actually apply?

    Continuous compounding uses A = P·e^(r·t) where e ≈ 2.71828. In practice, no bank compounds truly continuously — but the formula appears in:

  • Theoretical finance and options pricing (Black-Scholes uses continuous compounding).

  • Academic problems comparing nominal rates.

    • The difference between daily and continuous is fractions of a basis point — for all real-world savings and loan decisions, daily compounding is the practical ceiling.

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    When NOT to use these formulas

  • Variable-rate products (ARM mortgages, variable HELOCs, credit cards with intro APR): neither formula applies cleanly. Build a cash-flow model.

  • Amortizing loans (mortgages, auto loans): the compound formula overstates the final balance because each payment reduces principal. Use an amortization schedule.

  • Inflation-adjusted (real) returns: subtract expected CPI from your nominal rate.

  • Taxes: in taxable accounts, interest is taxed as ordinary income each year. Tax-advantaged accounts (401(k), Roth IRA, HSA) shield this — so the compound totals here are accurate for those wrappers.
    • Disclaimer: Los resultados son orientativos y no constituyen asesoramiento financiero individualizado. Antes de tomar decisiones con impacto, consultá con un asesor financiero registrado en la CNV o contador público matriculado.

    Frequently asked questions

    What is the key difference between simple and compound interest?
    Simple interest earns a fixed dollar amount every year based only on the original principal (I = P × r × t). Compound interest earns interest on the principal AND on interest already accumulated, so balances grow exponentially. On $10,000 at 7% for 30 years: simple interest yields $31,000 total; monthly compounding yields about $81,165 — a $50,165 difference from the same rate and time.
    Which financial products use simple interest vs compound interest?
    Simple interest: most auto loans, personal loans, student loans, US Treasury bills. Compound interest: credit cards (daily), high-yield savings accounts (daily, credited monthly), CDs (daily or monthly), mortgages (monthly amortization), bonds (semi-annual), 401(k) / IRA growth (effectively continuous reinvestment). Knowing which type applies to your product determines how your debt grows or savings accumulate.
    APR vs APY — what's the actual difference?
    APR (Annual Percentage Rate) is the nominal rate before compounding, required by the Truth in Lending Act for loans and credit cards. APY (Annual Percentage Yield) is the effective rate after compounding, required by the Truth in Savings Act for deposit accounts. APY = (1 + APR/n)^n − 1. Example: a 4.31% APR with daily compounding equals roughly 4.40% APY. Always compare APYs when shopping HYSAs, CDs, and money markets, and APRs when comparing loan offers.
    Is the Rule of 72 actually accurate?
    The Rule of 72 (years to double ≈ 72 ÷ annual rate) is accurate within about 1% for rates between 4% and 12%, which covers most realistic savings and investment scenarios. For higher rates (credit card territory at 20%+), the rule slightly overstates doubling time — true doubling at 24% is about 3.2 years vs the rule's 3.0. For continuous compounding the exact constant is 69.3 (ln(2) × 100), but 72 divides cleanly by 2, 3, 4, 6, 8, 9, and 12, making it the most useful mental-math version.
    Does daily compounding really beat monthly by much?
    Much less than most people think. On $10,000 at 5% for 10 years, daily compounding earns about $17 more than monthly — and $170 more on $100,000. The rate matters far more than frequency. A 4.50% APY HYSA compounded monthly will always beat a 4.40% APY HYSA compounded daily. When shopping savings accounts, focus on the APY number — it already bakes in the frequency, so you can compare apples to apples regardless of how often the bank compounds internally.
    Why does credit card debt explode so fast?
    Two reasons. First, credit card APRs sit at 20–29% — among the highest legal consumer rates anywhere. Second, credit cards compound daily, not monthly. The daily periodic rate on a 24.99% APR card is 0.0685% — applied to your balance every single day, giving an effective APY of about 28.4%. At the federal minimum-payment formula, a $5,000 balance at 24.99% takes roughly 22 years to pay off and costs about $10,400 in interest. This is why the CFPB recommends paying credit cards in full every month or aggressively above the minimum.
    What does the S&P 500 look like under compound growth historically?
    The S&P 500's long-run nominal CAGR including reinvested dividends has been roughly 10% per year going back to 1928, per NYU Stern and Robert Shiller data. Real returns (inflation-adjusted) are closer to 7%. That means $10,000 invested in a low-cost S&P 500 index fund and left alone for 30 years has historically grown to around $174,000 nominal. Past performance never guarantees future results, but the math is why advisors emphasize starting early and not touching the money.
    Are interest earnings on a HYSA or CD taxed?
    Yes. Interest earned in taxable bank accounts is reported on Form 1099-INT and taxed as ordinary income at your federal marginal rate, plus state income tax where applicable (per IRS Publication 550). A taxpayer in the 24% federal bracket earning 4.40% APY effectively earns about 3.34% after federal tax. Tax-advantaged wrappers shield this: Traditional 401(k)/IRA defer tax until withdrawal, Roth 401(k)/IRA make qualified withdrawals tax-free, and HSAs are triple-tax-advantaged. The compound totals shown in this calculator are pre-tax.
    Can I use this calculator for a mortgage?
    Not directly. A 30-year fixed mortgage uses monthly compounding, but each payment reduces principal — so plugging $300,000 at 7% for 30 years into the compound formula gives a balance that ignores payments. For mortgages, use an amortization calculator that schedules each monthly payment. As a rough check: at 7% over 30 years, total interest paid on a $300,000 loan is about $418,500 — the compound formula here is correct for lump-sum savings, CDs held to maturity, and bonds where principal isn't repaid until maturity.
    Is continuous compounding used in real banking products?
    Not in any product you'd encounter as a consumer. Continuous compounding (A = P·e^(r·t)) is mostly a theoretical tool used in options pricing models like Black-Scholes and in academic finance. No modern HYSA, CD, or money market account compounds truly continuously — the dollar difference between daily and continuous is fractions of a cent on typical balances, so for all practical retail finance decisions, daily is the ceiling.

    Methodology & trust

    Editorial

    Calculadora de finanzas revisada por el equipo editorial de Hacé Cuentas, contrastada con Consumer Financial Protection Bureau — APR vs APY explained, según nuestra política editorial y metodología.

    Updates

    Última revisión: June 20, 2026. Los parámetros se verifican periódicamente con las fuentes citadas.

    Privacy

    Calculations run 100% in your browser. We do not store or transmit your data.

    Limitations

    Indicative results. For critical decisions, consult a professional.

    📌 How to cite this calculator

    Rodríguez, M. (2026). Simple vs Compound Interest Calculator. Hacé Cuentas. https://hacecuentas.com/simple-interest-vs-compound-comparison

    Contenido bajo licencia CC-BY 4.0 — reutilizable citando la fuente con enlace a Hacé Cuentas.

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