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Compound Interest Calculator — Investment Growth Calculator

Calculate compound interest with optional regular contributions

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Compound Interest Calculator: Investment Growth Calculator

Table of Contents - Compound Interest

How to Use This Calculator - Compound Interest

Enter your Initial Principal—the starting amount you're investing or saving.

Enter the Annual Interest Rate as a percentage. This is the nominal rate before compounding effects.

Enter the Time Period in years—how long you'll invest.

Select Compounding Frequency from the dropdown: Annually (1), Semi-annually (2), Quarterly (4), Monthly (12), Weekly (52), or Daily (365). More frequent compounding produces slightly higher returns.

Optionally, enter an Additional Contribution—a recurring amount you'll add to the investment.

Select Contribution Frequency: how often you add contributions (monthly, quarterly, etc.).

Click "Calculate" to see results. The output displays:

  • Final amount (principal plus all growth)
  • Total interest earned
  • Effective annual rate (accounting for compounding)
  • Time to double your money
  • Year-by-year growth breakdown showing contributions and interest accumulation

The Core Principle: Exponential Growth

Compound interest means earning interest on interest. Unlike simple interest (calculated only on principal), compound interest recalculates on the growing balance, creating exponential rather than linear growth.

The basic formula: A = P(1 + r/n)^(nt)

Where A is final amount, P is principal, r is annual rate, n is compounding frequency, and t is years.

The magic of compounding intensifies over time. In early years, most growth comes from your principal. In later years, interest on accumulated interest becomes the dominant force. This is why starting early matters enormously—you're maximizing the time for compounding to work.

Albert Einstein allegedly called compound interest the eighth wonder of the world. Whether he said it or not, the mathematical reality is profound: money doubles, doubles again, and doubles again—each doubling adding as much as all previous growth combined.

How to Calculate Compound Interest Manually

Basic compound interest (no contributions):

A = P × (1 + r/n)^(n×t)

Example: $10,000 at 7% for 10 years, compounded monthly A = 10,000 × (1 + 0.07/12)^(12×10) A = 10,000 × (1.00583)^120 A = 10,000 × 2.0097 A = $20,097

Interest earned = $20,097 - $10,000 = $10,097

With regular contributions (future value of annuity):

For contributions made at the end of each period: FV = PMT × [((1 + r/n)^(n×t) - 1) / (r/n)]

Example: $200/month for 10 years at 7% FV = 200 × [((1.00583)^120 - 1) / 0.00583] FV = 200 × [1.0097 / 0.00583] FV = 200 × 173.08 FV = $34,616

Combined total: Total = Compound growth on principal + Future value of contributions Total = $20,097 + $34,616 = $54,713

Effective annual rate: EAR = (1 + r/n)^n - 1

Example: 7% compounded monthly EAR = (1 + 0.07/12)^12 - 1 = 7.23%

Rule of 72 (doubling time): Years to double ≈ 72 / Interest rate

Example: At 7%, doubling time ≈ 72/7 ≈ 10.3 years

Real-World Applications

Retirement planning. Project how much your 401(k) or IRA will grow. A 25-year-old investing $500/month at 7% for 40 years accumulates over $1.3 million—$240,000 in contributions, over $1 million in compound growth.

College savings. Calculate how much to save monthly for your child's education. Starting at birth with 18 years of growth makes the goal much more achievable.

Debt understanding (in reverse). Compound interest works against you on debt. A $5,000 credit card balance at 20% APR, making minimum payments, takes 30+ years to pay off and costs $15,000+ in interest.

Comparing investment accounts. Which is better: 5% compounded daily or 5.1% compounded annually? Calculate both to find the answer (spoiler: daily compounding at 5% yields about 5.127% effective rate).

Goal-setting. What monthly savings produces $100,000 in 15 years at 6%? Work backward to find the required contribution.

Scenarios People Actually Run Into

The late start penalty. At 25, you invest $500/month for 10 years, then stop (total: $60,000 invested). At 35, your friend starts investing $500/month for 30 years (total: $180,000 invested). At 65, you have more money despite investing less—because your money compounded longer.

The frequency illusion. Daily compounding versus monthly compounding on 5% over 30 years adds only about $1,000 to a $10,000 initial investment. Compounding frequency matters less than people think; rate and time matter more.

The inflation reality. Your 7% return feels great until you realize inflation is 3%. Your real return is about 4%. Over 30 years, a dollar's purchasing power drops by half. Compound interest must outpace inflation.

The early withdrawal disaster. Cashing out a $50,000 retirement account at age 35 doesn't just cost $50,000. It costs that $50,000 plus 30 years of growth—potentially $400,000+ by age 65.

The "I'll catch up later" fallacy. Doubling contributions later can't compensate for lost time. $500/month for 30 years beats $1,000/month for 15 years at the same rate.

Trade-Offs and Decisions People Underestimate

Time versus rate. Time is more powerful than rate for typical scenarios. Doubling your time invested often beats doubling your rate. A 5% return for 40 years beats 10% for 20 years on the same principal.

Contributions versus returns. Early in your investing career, contributions matter more than returns (you don't have much to compound). Later, returns dominate (your balance dwarfs annual contributions).

Risk versus return. Higher potential returns come with higher volatility. Stocks average 7-10% long-term but can drop 40% in a year. Bonds return 3-5% with less volatility. Your time horizon should match your risk tolerance.

Tax drag on compounding. Taxes on dividends and capital gains reduce effective compounding. Tax-advantaged accounts (401(k), IRA) let more of your returns compound.

Fees erosion. A 1% annual fee doesn't sound like much, but over 30 years it can consume 25% of your portfolio. Low-cost index funds preserve more of your compounding.

Common Mistakes and How to Recover

Confusing nominal and effective rates. An account advertising 12% APR compounded monthly actually yields 12.68% effective annual rate. Compare effective rates, not nominal.

Forgetting inflation. A 5% return with 3% inflation is really 2% real return. Adjust projections for inflation, or you'll overestimate future purchasing power.

Ignoring fees. Investment returns in calculators are gross returns. Net returns after 1-2% in fees are significantly lower, especially over long periods.

Overestimating future returns. Historical stock returns of 10% may not continue. Many financial planners now use 6-7% for projections. Conservative assumptions prevent disappointment.

Underestimating consistency's value. Missing contributions irregularly kills compounding momentum. Automating investments ensures consistency regardless of market conditions.

Related Topics

Present value. The reverse of future value—how much would you need today to have $X in the future? PV = FV / (1 + r/n)^(n×t)

Annuities. Regular payment streams, either paying in (accumulation) or paying out (distribution). Retirement savings and pension payouts are annuity calculations.

Bond yields. Bond pricing involves compound interest calculations. Yield to maturity considers coupon payments and price appreciation compounding to maturity.

Loan amortization. The opposite of savings compound interest—you're paying interest on a declining balance. Each payment covers interest plus principal reduction.

Continuous compounding. The theoretical limit of infinitely frequent compounding. Formula: A = Pe^(rt). In practice, daily compounding is nearly identical.

How This Calculator Works

Basic compound interest: A = P × (1 + r/n)^(n×t)

Where P = principal, r = annual rate (decimal), n = compounding frequency, t = years

With regular contributions: FV_annuity = PMT × [((1 + r/n)^(n×t) - 1) / (r/n)]

Total = Compound growth on principal + Future value of contributions

Effective annual rate: EAR = (1 + r/n)^n - 1

Time to double (Rule of 72): Years = ln(2) / (n × ln(1 + r/n))

Year-by-year breakdown: For each year from 1 to t:

  • Calculate compound growth on principal to that year
  • Calculate accumulated contributions and their growth
  • Display running totals of contributions and interest

Contributions are assumed to be made at the end of each period (ordinary annuity).

All calculations happen locally in your browser.

FAQs

What interest rate should I use for projections?

For stock investments, 6-7% is conservative (accounting for inflation reduction from historical 10%). For bonds, 3-4%. For savings accounts, 2-4% depending on current rates.

How does compounding frequency affect returns?

More frequent compounding produces higher returns, but the difference is small. Monthly versus annual compounding on 5% adds about 0.12% effective rate. Daily adds slightly more.

What's the difference between APR and APY?

APR is the nominal annual rate. APY (Annual Percentage Yield) is the effective rate after compounding. APY = (1 + APR/n)^n - 1. Always compare APY.

How much should I contribute monthly?

Financial advisors typically recommend saving 15-20% of income for retirement. Use the calculator to see what that produces and adjust your target or timeline accordingly.

Does compound interest apply to my savings account?

Yes, but at much lower rates than investments. A 2% savings account compounds, but $10,000 grows to only $12,190 after 10 years versus $19,672 at 7%.

What if my returns are variable each year?

This calculator assumes constant returns. Real investments fluctuate. Use average expected returns for planning, but understand that actual results will vary.

How do taxes affect compound interest?

Taxes on dividends, interest, or capital gains reduce what you keep and reinvest. Tax-advantaged accounts (401(k), IRA, Roth IRA) let full returns compound without annual tax drag.

Why does starting early matter so much?

Time is the most powerful variable in the compound interest formula. Ten extra years of compounding can double or triple your final amount, even with identical contributions and rates.

What's the Rule of 72?

A quick mental math trick: divide 72 by your interest rate to estimate years to double your money. At 8% return, money doubles in approximately 72/8 = 9 years. At 6%, about 12 years. This helps visualize long-term growth.

How does compound interest work against me with debt?

The same mathematics that grows investments also grows debt. Credit card balances at 20% compound against you—a $5,000 balance becomes $10,000 in about 3.6 years if untouched. Paying off high-interest debt is like earning that interest rate guaranteed.

Should I prioritize retirement accounts over taxable investing?

Generally yes, up to employer match (free money) and often up to contribution limits. Tax-advantaged accounts (401k, IRA) let your money compound without annual tax drag. A 7% return with 25% taxes on gains effectively becomes about 5.25% in a taxable account.

What about inflation's effect on my projections?

A 7% nominal return with 3% inflation is really about 4% real return. Over 30 years, a dollar loses roughly half its purchasing power. Use "real" (inflation-adjusted) returns when planning for future purchasing power, or plan to need more nominal dollars.

How do I account for market volatility in projections?

This calculator assumes constant returns, but real markets fluctuate. Consider running projections with different rates (optimistic, average, pessimistic) to understand the range of possible outcomes. Monte Carlo simulations offer more sophisticated probability modeling for retirement planning.