Compound Interest — Project Investment Growth

Solve For

Money In

Starting Principal

Regular Contributions

When frequency changes Deposit timing

Growth Factors

Annual Rate

Time Horizon

yrs

Compounding Frequency

Inflation

Tax Rate

Annual Fee

Volatility (σ)

Contribution Increase

%/yr

Account Type

Tax model

One-Time Deposits

Model an inheritance, bonus, or windfall at a specific year.

Schedule start date

Optional changes set a new contribution amount (0 pauses it) or add a deposit. Dates use actual days / 365; regular payments stay equally spaced in model years. A new amount applies on its date and restarts annual contribution increases.

Remember financial inputs on this device

Edits stay out of the URL. Remember is optional; existing saved inputs remain unchanged until you opt in or Reset. Shared links include the financial inputs you review.

Illustrative cash-flow model. Positive gains are taxed at each year-end (and the final stub) for taxable accounts; fees follow tax. Pre-tax withdrawal tax applies to the ending balance. Account eligibility, contribution limits and deductions are excluded. Find Time checks monthly dates through 100 years.

Model parameters; the deposit schedule, taxes and fees determine the result.

P$10,000 · r/n0.583% · nt120 · Monthly equivalent$500/mo → A—

Projected Wealth in 10 Years

Your money is growing! Enter contributions to see the crossover point.

Total Contributed

Net gain/loss

Passive Income/mo

Cost of Delay

Effective APY

0.00%

Years to Double

—

Compare lower / selected / higher return assumptions

Table and CSV use nominal balances; charts follow the selected display view.

Year	Balance	Interest	Principal	Added

Dividend return components (nominal USD)

Price gain/loss plus gross dividends minus dividend withholding equals net growth before separately modeled fees. Dividends are immediately reinvested; external deposits remain separate. Values are rounded for display; CSV includes raw event reconciliation.

Model year	Price gain/loss	Gross dividends	Dividend tax	Net dividends reinvested

Monthly detail

Balances at model-month checkpoints; annual tax and fee charges appear at period close. Values follow the selected nominal/today-dollar view. Deposits for a new period occur after its opening checkpoint.

Model month	Balance	Deposited	Net gain/loss

Wealth Breakdown

Principal

Interest

Named scenario snapshots

Snapshot name

Session only. Nominal ending balances can have different horizons and assumptions; a larger balance is not an account recommendation.

🎯 Goal Seeker

Find any unknown to hit your target. Select what to solve for:

Target Goal

Time (yrs)

Rate (%)

📊 Scenario Comparison

Conservative, Base, and Aggressive returns — using your current principal, contributions & time horizon.

🏦 Account Type Comparison

The same plan under three tax treatments — see how much a tax-advantaged account keeps for you.

⏪ What If You'd Started Earlier?

If you had started years ago…

⏰ Power of Starting Early

See exactly what you lose by waiting — using your current rate, contributions & time horizon.

📐 Rate × Time Sensitivity Matrix

Final balance at every combination of rate and time, using your current principal & monthly contributions.

🔥 FIRE Milestones

Based on your current inputs, here's when you'll hit key wealth milestones.

🏖️ Coast FIRE Number

FIRE target

Years to retirement

🪜 Contribution Ladder

Final balance at different monthly contribution levels, using your current rate & time horizon. Your current contribution is highlighted.

📈 Benchmark Comparison

Your rate vs. S&P 500, Real Estate, Bonds & HYSA — same principal & contributions over time.

4 min read 5 steps 7 terms 3 examples 9 FAQs g = (1+r/n)^n (APR); g = 1+r (effective); A = P g^t

The annual rate is nominal with n compounds per year.

YMYL Reviewed by Calculover Editorial Review · Updated 2026-05-10 · 4 sources

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Walk-through

How to Use This Calculator

5 steps

Enter Initial Investment

Input your starting principal amount.

Set Interest Rate

Nominal APR uses g=(1+r/n)^n; effective annual return uses g=1+r, so changing n does not change that entered annual return. Both use the same cash schedule. A 0% rate is valid.

Choose Compounding Frequency

Select how often interest compounds: daily, monthly, quarterly, or annually.

Add Monthly Contributions

Set Time Period

Enter the number of years for your investment horizon and view projected growth. Edits stay out of the URL. Remember is optional; existing saved inputs remain unchanged until you opt in or Reset. Shared links include the financial inputs you review.

⚡

Reference

Formula & Methodology

3 formulas

Compound Interest Formula

g = (1+r/n)^n (APR); g = 1+r (effective); A = P g^t

Nominal APR uses g=(1+r/n)^n; effective annual return uses g=1+r, so changing n does not change that entered annual return. Both use the same cash schedule. A 0% rate is valid.

Future Value with Regular Contributions

FV = P g^t + Σ PMT_k g^(t−t_k)

The annual rate is nominal with n compounds per year. Contribution frequency f determines actual dates, independently of n. End deposits occur at k/f; beginning deposits at (k−1)/f. A zero horizon adds no later deposits. This cash-flow sum precedes tax and fees; PMT_k includes regular and one-time deposits. Optional changes set a new contribution amount (0 pauses it) or add a deposit. Dates use actual days / 365; regular payments stay equally spaced in model years. A new amount applies on its date and restarts annual contribution increases.

After-Tax Effective Return

Tax = max(0, actual growth) × tax_rate; Balance_after_fee = (Balance−Tax)(1−fee)^Δt

Default annual positive-gain model. Positive actual growth is taxed at year-end and at the final partial horizon for taxable accounts; deposits are not gains and losses receive no tax credit. Fees follow tax. Pre-tax withdrawals tax the full ending balance separately.

Show derivation

Optional continuous dividend-only illustration

Dividend-only taxation replaces, rather than adds to, annual positive-gain taxation in the taxable scenario. Let L be the annual log return from the selected APR or effective-return convention, y the assumed continuous cash dividend yield and τ the assumed flat withholding rate: included-return basis uses Lnet=L−yτ, while price-return basis uses Lnet=L+y(1−τ). Deferred, Roth and HSA scenarios set current withholding to zero without asserting legal eligibility; pre-tax withdrawal tax remains separate. For each actual cashflow interval, modeled price gain plus gross dividends minus withholding gives net growth; reinvestment is immediate, external deposits are separate, and the existing fee schedule remains unchanged. With $1,000, zero entered total return, 4% continuous yield, 25% withholding and one year without fees or deposits, the ending balance is $990.05, not $1,030.45; the latter uses the different price-return basis. The raw event CSV exposes reconciliation; displayed component amounts are rounded separately. Real payout dates, qualified rates, sale tax and tax-lot basis are excluded.

Lnet = L−yτ (included); Lnet = L+y(1−τ) (price)

✓

YMYL

Trust, Methodology & Sources

Reviewed by Calculover Editorial Review · Updated 2026-05-10 · 4 sources

Editorial accountability

Author: Quinn Sumner - Editor

Owner: Quinn Sumner - Editorial owner

Reviewer: Calculover Editorial Review - Source and limitation review

Last reviewed: 2026-05-10

Last verified: 2026-05-10

Data effective: 2026-05-10

Methodology

Default annual positive-gain model. The annual rate is nominal with n compounds per year. Contribution frequency f determines actual dates, independently of n. End deposits occur at k/f; beginning deposits at (k−1)/f. A zero horizon adds no later deposits. Positive actual growth is taxed at year-end and at the final partial horizon for taxable accounts; deposits are not gains and losses receive no tax credit. Fees follow tax. Pre-tax withdrawals tax the full ending balance separately. Nominal APR uses g=(1+r/n)^n; effective annual return uses g=1+r, so changing n does not change that entered annual return. Both use the same cash schedule. A 0% rate is valid. Optional changes set a new contribution amount (0 pauses it) or add a deposit. Dates use actual days / 365; regular payments stay equally spaced in model years. A new amount applies on its date and restarts annual contribution increases.

Assumption: Compound Interest relies on the values the user enters and does not independently verify income, balances, legal status, policy terms, or market quotes.

Assumption: Positive actual growth is taxed at year-end and at the final partial horizon for taxable accounts; deposits are not gains and losses receive no tax credit. Fees follow tax. Pre-tax withdrawals tax the full ending balance separately.

Assumption: Actual market returns are volatile and can differ materially from the constant-rate or scenario assumptions.

Limitations & guidance

The 500 paths use independent annual lognormal assumptions and the same cash schedule. Zero volatility matches the deterministic model. Percentiles and target frequencies describe the chosen model, not calibrated confidence or future market probabilities.

Actual results depend on market performance, timing, taxes, fees, liquidity, reinvestment, and risk tolerance.

This calculator provides projections for educational purposes only. Results are estimates based on assumed constant rates and do not account for market volatility, taxes, or investment fees beyond those explicitly entered. Past performance does not guarantee future results. Consult a licensed financial advisor (CFP®) before making investment decisions.

Professional guidance: Compound Interest is for investment math education only and is not investment, tax, legal, or financial advice. Consider risk, fees, taxes, and suitability before acting.

Primary sources

Compound Interest Calculator - Investor.gov

Introduction to Investing - Investor.gov

FV function - Microsoft

Reinvested dividends - Internal Revenue Service

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Glossary

Key Terms Explained

7 terms

Compound Interest Interest calculated on both the initial principal and accumulated interest from previous periods — "interest on interest."

APY vs APR APY (Annual Percentage Yield) includes the effect of compounding; APR does not. APY is always ≥ APR.

Crossover Point The year when cumulative interest earned exceeds total contributions — your money is growing faster than you can save.

Fee Drag The cumulative loss in final balance caused by annual management fees compounding away from your portfolio.

Monte Carlo A probabilistic simulation using random annual returns to model the range of possible outcomes with confidence intervals.

Safe Withdrawal Rate (SWR) The 4% rule: withdrawing 4% of your portfolio annually is historically sustainable over 30+ year retirements.

FIRE Financial Independence, Retire Early — the milestone at which your portfolio can sustain indefinite withdrawals via the 4% rule.

👥

Scenarios

Real-World Examples

3 worked examples

👤

Alex

Basic Savings Growth

Principal $10,000 Annual Rate 7% Compounding Monthly Time Period 10 years

With no later deposits, tax or fees, $10,000 at nominal 7% compounded monthly becomes $20,096.61 after 10 years. The $10,096.61 gain depends on a constant assumed rate, not a market forecast.

👩

Sarah

Monthly Contributions Power

Principal $10,000 Monthly Contribution $500 Annual Rate 7% Time Period 30 years

Assuming monthly compounding and end-month deposits, $10,000 plus $500 monthly for 30 years at nominal 7% becomes $691,150.47. Deposits total $190,000; net gain is $501,150.47 before tax and fees.

👨

Marcus

Fee Drag Impact

Principal $10,000 Monthly Contribution $500 Annual Rate 7% Annual Fee 1%

Using 30 years, monthly compounding and end-month $500 deposits, a 1% year-end fee reduces $691,150.47 to $558,595.81: a $132,554.66 ending-balance gap. Tax and investment-product differences are excluded.

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Reference

Cite This Calculator

APA & MLA

Use either format to cite this calculator in a paper, report, or resource list.

APA

MLA

📄

Deep Dive

The Power of Compound Interest

4 chapters · 4 min read

Why Starting Early Matters More Than Starting Big

Each later case shortens the same deposit schedule. Cash before starting is excluded; one-time deposits remain relative to the new start. Outcomes can improve or worsen with losses.

Check the active fields and model bounds. Time is searched at monthly checkpoints through 100 years; the rate search is above −100% through 200%.

The Hidden Cost of Investment Fees

Default annual positive-gain model.

Positive actual growth is taxed at year-end and at the final partial horizon for taxable accounts; deposits are not gains and losses receive no tax credit. Fees follow tax. Pre-tax withdrawals tax the full ending balance separately.

Monte Carlo: Planning for Uncertainty

Tax-Advantaged Compounding

Default annual positive-gain model.

Equal cash deposits assumed. Eligibility, limits, deductions and qualified-withdrawal rules are excluded.

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Questions

Frequently Asked Questions

9 questions

What exactly is compound interest?+

Compound interest is the addition of interest to the principal sum of a loan or deposit — interest on interest. It results from reinvesting interest rather than paying it out, so interest in the next period is earned on the principal sum plus previously accumulated interest.

How do the 5-way Solve Modes work?+

Required deposit per selected contribution period, using the main account, tax, fee, step-up and one-time deposit assumptions. Check the active fields and model bounds. Time is searched at monthly checkpoints through 100 years; the rate search is above −100% through 200%.

What does Monte Carlo simulation show?+

How does fee drag affect my returns?+

What is the difference between APR and APY?+

Nominal APR uses g=(1+r/n)^n; effective annual return uses g=1+r, so changing n does not change that entered annual return. Both use the same cash schedule. A 0% rate is valid.

How does inflation impact my total savings?+

Inflation erodes the purchasing power of your money. Enable "Inflation" in Advanced Settings to see the real value of your future wealth in today's dollars. At 2.5% inflation, $1M in 30 years has the purchasing power of only about $477K today.

What does the Frequency Comparison chart show?+

What are FIRE Milestones?+

FIRE (Financial Independence, Retire Early) milestones show how many years until your balance reaches key thresholds ($100K, $500K, $1M, $2M, $5M) based on your current inputs. These appear in the Wealth Projector tab and update live as you change your inputs.

How does the optional dividend-only model avoid double counting?+

Choose whether the entered return already includes reinvested dividends or represents price return only; the first choice allocates dividends within the entered return rather than adding them again. Continuous distributions, immediate reinvestment and a flat assumed withholding rate are model assumptions, not a payout-calendar or tax-eligibility determination. This model replaces annual positive-gain tax for taxable accounts, while the separate pre-tax withdrawal assumption remains and deferred, Roth and HSA scenarios have no current dividend withholding. The component ledger and CSV use the same cashflow schedule, and the retained historical total-return series always uses the included-dividend basis.

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How to Use This Calculator

Enter Initial Investment

Set Interest Rate

Choose Compounding Frequency

Add Monthly Contributions

Set Time Period

Formula & Methodology

Optional continuous dividend-only illustration

Trust, Methodology & Sources

Key Terms Explained

Real-World Examples

Cite This Calculator

The Power of Compound Interest

Why Starting Early Matters More Than Starting Big

The Hidden Cost of Investment Fees

Monte Carlo: Planning for Uncertainty

Tax-Advantaged Compounding

Frequently Asked Questions

Get a branded PDF of your results

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