Compound Interest Calculator: APR/APY, Fees, Taxes & Inflation
Project how a starting deposit and steady contributions compound over time — then layer in the real-world frictions that change the answer: APR versus APY, compounding and contribution frequency, fees, taxes, inflation and a yearly contribution raise.
Adjust the inputs and select Calculate for a full breakdown.
Year-by-year growth, fees & balance
Compare Common Scenarios
How the numbers shift across typical situations for this calculator:
| Scenario | Future value (net) | Total contributions | Effective annual rate | Future value (real, today’s $) |
|---|---|---|---|---|
| Index fund · $10k + $500/mo · 7% APR · 1% fee · 15% tax · 30yr | $506,045.69 | $190,000.00 | 7.23% | $208,484.12 |
| High-yield savings · $5k + $200/mo · 4% APY · 15yr | $57,936.13 | $41,000.00 | 4.00% | $37,187.00 |
| Pay-rise saver · $300/mo +2%/yr · 8% · start-of-month · 25yr | $340,156.41 | $115,309.08 | 8.30% | $162,460.59 |
| Lump sum · $20k · 6% continuous · 15yr | $49,192.06 | $20,000.00 | 6.18% | $31,574.51 |
How This Calculator Works
Enter your starting balance, the quoted rate, and the contribution. Say whether the rate is an APR (a nominal rate compounded at the frequency you pick) or an APY (already effective), and the calculator derives the correct effective annual rate so frequency is never double-counted. The balance is then simulated one step per contribution period, adding each deposit at the start or end of the period as you choose. A percentage fee drags the balance each step, a tax estimate is applied to the gain, and the final figure is also shown in today’s dollars after inflation. The schedule separates contributions, interest and fees year by year.
The Formula
Future Value with Variable Contributions, Fees, Taxes & Inflation
P = principal, PMT = contribution (stepped up yearly by the increase rate), m = compounding periods/yr, c = contributions/yr, EAR = effective annual rate; a periodic fee drags the balance, tax applies to net gains, and inflation deflates the result to today’s dollars.
Worked Example
Start with $10,000 and add $500 a month for 30 years at a 7% APR compounded monthly. Gross, the balance reaches about $691,150 on $190,000 of contributions. Now charge a 1% annual fee and a 15% tax on gains: fees cost roughly $129,300 (including the growth they forgo) and tax another $55,800, leaving about $506,000 net — a vivid illustration of how a single percentage point of fee compounds against you over decades.
Key Insight
The quoted rate is only the starting point. Converting APR to its effective yield, and then subtracting fees, taxes and inflation, often moves the realistic outcome by a third or more — which is why a calculator that stops at the gross number flatters every projection.
The Rule of 72: how long for money to double
A simple shortcut every saver should know: divide 72 by your annual return rate to get the years it takes for money to double. At 6%/year: 72/6 = 12 years to double. At 8%: 72/8 = 9 years. At 10%: 72/10 = 7.2 years. At 3%: 72/3 = 24 years.
This isn't exact mathematically — the precise number is ln(2)/ln(1+r) — but Rule of 72 is accurate within ~5% for rates between 4% and 15%. Beyond this range, use 70 or 76 as alternative numerators. The true mathematical limit is the 'Rule of 69.3': as the rate approaches zero (or with continuous compounding), doubling time approaches ln(2)/r, and ln(2) ≈ 0.693, so 69.3 is the exact numerator in that limit. The 'Rule of 70' is not exact — it is just the rounder, more convenient stand-in that stays a good practical approximation, while 72 is preferred for mental math because it divides cleanly by more rates.
Practical application: if you want $1M by 65 and you're 25 (40 years), you need money to double roughly 3-4 times — meaning either large early contributions OR a higher growth rate. At 8%, 40 years allows ~4.4 doublings — turning $50,000 into $1M+ with no further contributions. At 4%, only ~2.5 doublings — same $50,000 reaches just $240,000. The arithmetic explains why early-decade investing dominates.
Compounding frequency: daily vs monthly vs annual — how much it matters
Most savings products advertise an interest rate alongside a 'compounding frequency': annual, monthly, daily, or continuous. The frequency affects your real return — but less than most savers think.
Concrete comparison: $10,000 at 5% APR for 10 years. Annual compounding: $16,289. Quarterly: $16,436 (+0.9%). Monthly: $16,471 (+1.1%). Daily: $16,487 (+1.2%). Continuous: $16,487 (+1.2%). The gap between daily and continuous is essentially zero — the gap between annual and daily is just 1.2% over 10 years.
Banks often quote 'APY' (Annual Percentage Yield) which already accounts for compounding frequency. Two products quoting 5% APY are equivalent regardless of underlying frequency. Compare APYs, not APRs. The compounding-frequency math is mostly marketing — focus on the headline APY and the credit quality of the institution instead.
Starting early vs catching up later: the brutal arithmetic
The single most important number in personal finance: each year of compounding multiplies your wealth more than the previous year. Concrete example: two investors saving for retirement at 65, both earning 7% compounded monthly with contributions added at the end of each month — the exact assumptions this calculator uses.
Early investor: contributes $200/month from age 25 to 35 ($24,000 total), then stops contributing and lets the balance compound untouched. The $34,617 built by age 35 grows to ~$280,968 by 65. Late investor: contributes $200/month from 35 to 65 ($72,000 total — 3× as much). By 65: ~$243,994. The early investor still comes out ahead — by about 15% — despite paying in only one-third as much money. (You can reproduce both figures above by running the calculator: $0 start · $200/mo · 7% · 10yr for the first leg, then feeding that balance in as the starting amount with $0/mo for the next 30 years.)
Mathematics: each dollar contributed at age 25 has 40 years to compound — a multiplier of ~16.3× at 7% compounded monthly. Each dollar contributed at 55 has just 10 years left, a multiplier of only ~2.0×. That roughly 8× gap in how hard each early dollar works is why a front-loaded decade of saving can out-earn three decades of catching up. Time is the dominant input to compound interest — start the contribution flow as early as possible, even at small amounts.
How $10,000 grows with different rates and time (annual compounding)
Future value of a one-time $10,000 investment at varying annual returns. No additional contributions. Shows the dramatic effect of small rate differences over decades.
| Rate | 10 years | 20 years | 30 years | 40 years |
|---|---|---|---|---|
| 3% | $13,439 | $18,061 | $24,273 | $32,620 |
| 5% | $16,289 | $26,533 | $43,219 | $70,400 |
| 7% | $19,672 | $38,697 | $76,123 | $149,745 |
| 10% | $25,937 | $67,275 | $174,494 | $452,593 |
| 12% | $31,058 | $96,463 | $299,599 | $930,510 |
The difference between 7% and 10% return over 40 years: 3× more money. Over 10 years: only 1.3× difference. Time amplifies rate differences dramatically. The ~10% nominal / ~7% real figure often cited for diversified stock indexes is a historical benchmark, not a forecast — future returns are unknown and can be lower or negative; treat these rows as illustrations of how rate and time interact, not as expected outcomes.
Simple vs Compound Interest
A fixed, reproducible scenario: $10,000 initial + $200/month, 7% APR, 20 years, monthly compounding, end-of-month contributions, no fees, taxes or inflation. 'Simple interest' means the stated 7% rate applied linearly with no compounding — the starting deposit earns it for the full 20 years and each $200 deposit earns it only for the months it stays invested; 'compound interest' lets that interest earn interest too. Total contributions are $58,000 in both columns.
| Measure | Simple interest | Compound interest | Difference |
|---|---|---|---|
| Final balance | $105,460.00 | $144,572.72 | $39,112.72 |
| Total interest | $47,460.00 | $86,572.72 | $39,112.72 |
Same deposits and rate over 20 years: compounding reaches $144,572.72 versus $105,460.00 under simple interest — an extra $39,112.72 (37.1% more) earned purely because interest itself begins earning interest.
The Cost of Waiting: Start Now vs Later
A $5,000 start with $400/month at 8% aimed at a 30-year finish line. Delaying the start keeps the end date fixed, so each year of waiting removes a year of contributions and compounding.
Starting today, this plan reaches $650,822.43 in 30 years. Each year of delay shortens the runway:
| Delay | Final balance | Lost growth | Catch-up contribution/mo |
|---|---|---|---|
| 1 year | $596,346.03 | $54,476.40 | $439.92/mo (+$39.92) |
| 3 years | $499,598.25 | $151,224.18 | $532.49/mo (+$132.49) |
| 5 years | $417,111.44 | $233,710.99 | $645.75/mo (+$245.75) |
| 10 years | $260,242.18 | $390,580.25 | $1,063.10/mo (+$663.10) |
“Lost growth” is what the delay costs versus starting now; the catch-up column is the contribution/mo needed over the shorter remaining horizon to still reach $650,822.43 (the bracketed figure is the extra on top of the original $400.00/mo).
Goal Solver: How to Reach $1,000,000
Working backwards from a $1,000,000 target. Starting at $10,000 and 7%, the solver finds the contribution, the starting deposit, or the time required — one lever at a time, holding the others fixed.
Target: $1,000,000.00. Starting from $10,000.00 at 7% over 25 years, here is what it takes — solving one lever at a time, holding the others fixed:
| Lever to solve | Required value | Holding fixed |
|---|---|---|
| Contribution/mo | $1,163.78/mo | $10,000.00 start · 25 yr |
| Starting deposit | $132,213.66 | $300.00/mo · 25 yr |
| Time needed | 40y 9m | $10,000.00 start · $300.00/mo |
Each row solves for one input by bounded numerical search (bisection, capped iterations) against the calculator’s own model, so the answers stay consistent with the projection above. Edge cases — a 0% rate, a target already met, or one unreachable within limits — are reported in words rather than a misleading number.
Frequently Asked Questions
What is compound interest?
Compound interest is interest calculated on both your original money and the interest already added to it. Over time the interest-earning base keeps growing, so each period adds slightly more than the one before.
How is compound interest different from simple interest?
Simple interest is paid only on your original deposit, so a balance grows in a straight line. Compound interest is paid on the deposit plus all prior interest, so the balance curves upward and accelerates.
How often should interest compound?
You choose: the compounding frequency control offers annual, semi-annual, quarterly, monthly, daily or continuous. More frequent compounding raises the effective yield slightly — the calculator shows that as the effective annual rate — but the rate and the time horizon matter far more than the interval. If you enter the rate as an APY, the compounding frequency no longer changes the result, because an APY is already the effective annual figure.
Does the calculator account for inflation?
Yes. Enter an inflation rate and the calculator reports both the nominal future value and the real (today's-dollars) value, which deflates the net result by inflation over the horizon. The default inflation rate is the cited CPI benchmark; treat any growth at or below inflation as merely keeping pace with rising prices rather than building real wealth.
What rate should I enter?
Use a rate that matches where the money sits — a deposit rate for cash, or a long-run market return for invested funds. The default reflects a cited historical market benchmark, which is a reference point, not a forecast or a promise: future returns are unknown and can be lower or negative.
Can I rely on these projections?
Treat them as illustrations, not promises. Actual returns fluctuate year to year, and a steady average rate smooths over the ups and downs a real account would experience.
Simple vs compound interest — how big is the difference?
Simple interest pays only on the money you put in, so it grows in a straight line; compound interest pays on your deposits plus all the interest already earned, so it curves upward. The Simple vs Compound module below runs both on identical deposits and rate so you can read the gap directly — over a few decades compounding routinely earns tens of percent more from the very same contributions.
What does it cost to wait a few years before starting?
More than most people expect, because the dollars you skip are the ones with the most time to compound. The Cost of Waiting module keeps the same end date and shows, for delays of 1, 3, 5 and 10 years, the lower final balance, the growth you forfeit, and the larger contribution you would then need to still hit the original target.
How much do I need to save to reach a target?
The Goal Solver module works backwards from a target balance. It uses a bounded numerical search against this calculator’s own model to report the contribution, the starting deposit, or the time required — solving one lever while holding the others fixed — and states plainly when a goal is already met or can’t be reached within sensible limits.
What is the difference between APR and APY here?
APR (annual percentage rate) is a nominal rate: the calculator compounds it at the frequency you select, so its effective yield ends up slightly higher than the headline number. APY (annual percentage yield) is already the effective yearly figure, so it is used as-is and the compounding frequency no longer affects it. Use the rate-type control to match how your rate was quoted; the result panel shows the resulting effective annual rate either way, so you can see the two on the same footing.
Does it matter whether contributions are made at the start or end of each period?
Slightly, and the calculator lets you pick. A start-of-period contribution (an 'annuity due') earns one extra period of growth compared with an end-of-period contribution (an 'ordinary annuity'), so over long horizons the start-of-period option finishes a little higher for the same money. The effect is small next to the rate and the time horizon, but it is real and the model applies whichever timing you choose.
What is the difference between the nominal and real (today's-dollars) value?
The nominal value is the raw future balance in future dollars. The real value restates that figure in today's purchasing power by removing assumed inflation over the horizon. A $1,000,000 nominal balance in 30 years buys far less than $1,000,000 buys now, so the real value is the more honest gauge of what the money will actually be worth — plan against it, not the headline nominal figure.
How are fees and taxes handled?
Both are optional and transparent. The fee is charged as a constant percentage of the balance each period and reported as 'estimated fees' — the full cost, including the growth those fees would otherwise have earned. Tax is a single flat rate applied to the post-fee gain at the end of the horizon and shown as 'estimated taxes'. The figures reconcile: net value equals gross value minus fees minus taxes. They are simplifications — real fee schedules and tax rules are more complex — so treat them as estimates, not tax advice.
Why does my estimate differ from my bank or brokerage statement?
A statement reflects what actually happened: your real daily balances, the institution's own day-count and interest-posting rules, dividends and price changes, and any fees or taxes charged in real time. This calculator instead projects forward from a single steady assumed rate with simplified fee, tax and inflation assumptions. Small differences in compounding convention, posting timing and realised return compound over years, so a projection and a statement will rarely match to the dollar — the projection is a planning estimate, not a record of an account.
References & Authoritative Sources
- U.S. Securities and Exchange Commission — Investor.gov — Compound Interest — investor education · consulted May 31, 2026 · Purpose: the compound-interest concept. Federal investor-education reference for how interest earns interest over time. Consulted to define the concept, not as a source of returns.
- Truth in Savings Act — 12 CFR Part 1030 (Regulation DD) — Statutory basis for APY disclosure · consulted May 31, 2026 · Purpose: APR vs APY disclosure. Federal regulation requiring banks to disclose APY and the formula behind it, so the calculator's APR↔APY handling matches the legal standard.
- FDIC — Federal Deposit Insurance Corporation — Compounding frequency and APY calculation · consulted May 31, 2026 · Purpose: APR vs APY methodology. Federal regulator's consumer guidance on how compounding frequency turns a nominal rate into an effective yield.
- U.S. Bureau of Labor Statistics — Consumer Price Index (CPI-U) — Consumer Price Index — All Urban Consumers · consulted May 31, 2026 · Purpose: inflation benchmark. Source of the default inflation rate used only to express results in today's dollars; a measured, dated figure, not a forecast.
- S&P Dow Jones Indices — S&P 500 — long-run annualized total return · consulted December 31, 2025 · Purpose: historical market benchmark. Basis for the default equity-return input. This is a historical benchmark, not a forecast — past returns do not predict future results and equity values can fall as well as rise.
Related Calculators
Data Sources & Benchmarks
This calculator draws on 3 independent, dated sources. The starting values for annual rate and inflation rate are taken from the benchmarks below and refresh whenever the snapshots are updated. Sources are used to fix regulatory definitions (how APR and APY must be disclosed) and to supply dated, historical benchmarks for the default inputs — they are reference points, not forecasts of future returns.
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Assumptions
- Returns are applied at one constant rate every period; real markets vary year to year and can be negative.
- Interest compounds at the frequency you select; contributions recur at the frequency you select and are equal in size, apart from the optional once-a-year step-up applied on each contribution anniversary.
- An APR is treated as a nominal rate compounded at the chosen frequency; an APY is treated as already effective, so compounding frequency does not change it.
- Fees are charged as a constant percentage of the balance each period; taxes are a single flat rate applied to the post-fee gain at the end of the horizon; inflation is one constant annual rate used only to express the result in today's dollars.
- Time is measured in whole contribution periods, so a horizon is rounded to the nearest period boundary.
- In the Simple vs Compound comparison, 'simple interest' means the stated annual rate applied linearly with no compounding: the starting deposit earns it for the full term and each contribution earns it only for the time it stays invested.
Limitations & Disclaimer
This is an educational tool, not financial advice. It does not account for your personal circumstances, and no result is a guarantee.
- No guarantee: projections are illustrations, not promises — actual returns fluctuate and can be negative in any period.
- No personal advice: this tool does not know your tax bracket, account type, risk tolerance or goals, and is not a recommendation.
- Returns vary: a single steady rate smooths over the sequence-of-returns risk a real portfolio experiences.
- Simplified fees and taxes: a flat percentage fee and a flat tax on gains ignore tiered or flat-dollar fees, trading costs, tax brackets, holding-period rules and jurisdiction.
- Inflation is a single assumed rate; realised inflation differs and is itself uncertain.
- Figures may differ from a bank or brokerage statement, which uses your actual daily balances, the institution's own day-count and posting rules, and real (not assumed) returns.
Methodology & Review
The balance is simulated one step per contribution period — not a single closed-form formula — so every contribution, the chosen timing, the fee drag and the annual step-up are applied in sequence. APR is converted to an effective annual rate via (1 + APR/m)^m − 1 (e^APR − 1 when compounding is continuous); APY is treated as already effective so the compounding frequency is never double-counted. A periodic fee drags the balance each step; taxes are estimated as the chosen rate applied to the post-fee nominal gain; the real value deflates the net result by inflation over the horizon. Every formula in the engine is re-verified on each build against a fixed golden-test suite, so a numerical regression fails the build before it can publish. Fees, taxes and inflation are simplifying estimates and do not constitute tax advice.
Methodology, sourcing and internal review by Ugo Candido, Founder & Editor-in-Chief (as of ). External financial review: not yet completed. Internal technical review: performed through contract-gated golden tests on each build.
Version history
- · 1.0 — Initial release: monthly compounding of a starting balance plus a fixed monthly contribution.
- · 1.1 — Accuracy pass: corrected the Rule-of-72/70 explanation to the mathematically exact Rule-of-69.3 limit, and expanded the golden-test coverage.
- · 2.0 — Added APR/APY rate types, selectable compounding and contribution frequency, contribution timing, fees, taxes, inflation (nominal and real output) and an annual contribution increase.
- · 2.1 — Added the Simple-vs-Compound, Cost-of-Waiting and Goal-Solver modules, each solved by bounded numerical search against the calculator's own model.
Reviewed according to the CalcDomain Editorial Policy & Calculator Methodology. We document formulas, edge cases, sources, update dates, and correction paths for calculator pages.
Updated