Compound Interest Calculator

Initial investment:

Enter dollars only, e.g. 10000 for a $10,000 starting balance.

Monthly contribution:

Enter 0 for lump-sum growth, or a monthly savings amount such as 200.

Annual interest rate:

Use percent form, e.g. 5.25 for a 5.25% annual rate.

% / yr

Compound frequency:

Choose the rule from the account or quote: monthly, daily, annual, or continuous.

Investment length:

Enter whole years plus 0-11 extra months; 0 months shows the starting balance only.

years months

Target balance:

Enter a target dollar amount, or 0 to turn off goal tracking.

Annual contribution:

Enter annual dollars, e.g. 1200 to add $100 per month.

Contribution timing:

Use Beginning for deposits made before monthly interest; End for after.

Annual contribution growth:

Enter a yearly percent increase, e.g. 3 for deposits that rise 3% each year.

% / yr

Tax rate on interest:

Enter 0-100; use 0 for tax-free or tax-deferred interest.

Inflation rate:

Enter expected annual inflation, e.g. 2.5; use 0 to hide inflation drag.

% / yr

Annual account fee:

Enter the fund or account fee percent, e.g. 0.25 for 0.25% per year.

% / yr

Monthly account fee:

Enter the recurring account fee in dollars, e.g. 5; use 0 for none.

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Checkpoint	Invested ($)	Ending ($)	Real ($)	Goal progress	Copy
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Year	Invested ($)	Interest ($)	Fees ($)	Real ($)	Ending ($)	Copy
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Month	Deposit ($)	Interest ($)	Fees ($)	Ending ($)	Copy
{{ row.label }}	{{ money(row.deposit) }}	{{ money(row.interest) }}	{{ money(row.fee) }}	{{ money(row.ending) }}

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A quoted interest rate is only the starting point for a savings projection. The final balance also depends on when interest is credited, whether new deposits arrive before or after growth, how long the money stays in the account, and whether taxes, fees, or inflation reduce the value that remains.

Compound interest means that interest left in the account becomes part of the base that can earn more interest later. The effect is small at first and grows with time. A higher rate helps, but a steady deposit pattern and a longer horizon can matter just as much because they give more dollars more months to participate in compounding.

Principal: The starting money already available to earn interest.
Contributions: New deposits added during the projection, either monthly or through an annual amount spread across months.
Nominal rate: The stated annual rate before compounding frequency changes its one-year effect.
Effective annual yield: The one-year growth rate after the chosen compounding rule is applied.
Real balance: The projected balance discounted by the inflation assumption to estimate purchasing power.

Principal and deposits flow into compounding interest, then tax, fees, and inflation affect the final balance. — A projection is built from money added, growth credited, costs deducted, and purchasing-power adjustment.

Compounding frequency is often misunderstood. Monthly compounding at a 5% nominal annual rate produces a slightly higher effective annual yield than annual compounding at the same stated rate. Continuous compounding is the mathematical limit of increasingly frequent crediting. More frequent crediting can help, but a monthly account fee, a tax haircut on interest, or inflation can more than offset the difference.

A compound-interest projection is a planning model, not a promise from a bank or brokerage. It is useful for comparing assumptions, estimating goal timing, and spotting fee or inflation drag. It does not settle market risk, changing rates, contribution limits, withdrawal rules, tax eligibility, penalties, or whether a product is suitable for a specific person.

How to Use This Tool:

Start with the assumptions you can defend, then use the schedule and comparison outputs to see which assumption drives the result.

Enter Initial investment and Monthly contribution. Use 0 for either field when the plan is a pure lump sum or a pure recurring deposit pattern.
Set Annual interest rate and Compound frequency. The frequency changes Effective annual yield even when the nominal rate is unchanged.
Enter Investment length in whole years plus 0 to 11 extra months. A zero-month horizon keeps the projection at the starting balance and triggers a warning.
Set Target balance when you want the goal status, gap, and milestone rows. Enter 0 when you only want a growth projection.
Open Advanced for Annual contribution, Contribution timing, contribution growth, tax on interest, inflation, percentage account fees, and fixed monthly fees.
Beginning-of-month contributions earn growth sooner than end-of-month contributions; use the setting that matches how deposits actually arrive.
Review warnings before relying on the balance. Target not reached, inflation above modeled growth, projected fees above interest, and zero-month length all change how the result should be read.
If a warning appears, change one assumption at a time so the comparison rows still show what caused the improvement.
Read Projection Snapshot first, then use Milestone Runway, Annual Path, Monthly Path, Balance Mix, Growth Runway, and Rate Sweep when you need schedule detail or sensitivity checks.

Interpreting Results:

Ending balance is the nominal projected account value. Ending balance (real) discounts that value by the inflation assumption, so it is the better field for purchasing-power planning. Total invested capital, Recurring contributions, Compounded gain, and Fees charged explain how the balance was built.

Effective annual yield reflects the nominal rate and compounding frequency before tax, fees, and inflation.
Real annual yield compares effective annual growth with inflation. A negative value means the model loses purchasing power.
IRR (annualized) includes deposit timing and ending value, so it is useful when recurring contributions are large.
+1 pp rate ending, +12 months ending, and the no-fee scenario show which assumption has the most leverage.

Do not treat a large nominal balance as a financial plan by itself. Verify the real balance, warning rows, goal gap, and monthly or annual path before using the projection for a savings or investment decision.

Technical Details:

The nominal annual rate is converted into the growth rule used by the projection. Annual, semiannual, quarterly, and monthly settings create scheduled interest-crediting events. Daily compounding and continuous compounding use an equivalent monthly rate so the month-by-month path remains readable while the annual yield still follows the selected compounding rule.

Deposits, taxes, fees, and inflation are applied along that monthly path. Beginning contributions are added before that month's growth; end contributions are added afterward. Tax reduces each credited interest amount before it compounds. The percentage account fee is divided across months, the fixed monthly fee is added to it, and the fee deduction is capped so the balance does not go below zero. Real balances divide nominal balances by the inflation factor for the elapsed time.

Formula Core:

The first equations convert the nominal annual rate into an effective annual yield. The recurrence advances the balance through each modeled month.

\begin{array}{lcl} y_{eff} & = & {(1 + \frac{r}{n})}^{n} - 1 \\ y_{eff} & = & e^{r} - 1 for continuous compounding \\ B_{m} & = & (B_{m - 1} + D_{pre}) \times (1 + i_{m} \times (1 - t)) - F_{m} + D_{post} \\ B_{real} & = & \frac{B_{end}}{{(1 + π)}^{\frac{M}{12}}} \end{array}

Compound interest formula symbols
Symbol	Meaning	Related input or output
r	Nominal annual rate as a decimal	Annual interest rate
n	Compounding events per year	Compound frequency
i_m	Scheduled monthly credit rate, equivalent monthly rate, or 0 when no event is due	Monthly path interest
D_pre and D_post	Contribution added before or after monthly growth	Contribution timing
t	Tax rate applied to credited interest	Tax rate on interest
F_m	Monthly percentage and fixed fee deduction, capped at the current balance	Annual account fee and monthly account fee
π	Annual inflation assumption	Inflation rate and ending balance (real)

A 5% nominal rate compounded monthly gives an effective annual yield of about 5.116%. With 2.5% inflation, the real annual yield is about 2.552% before tax and fees. That gap explains why a nominal balance can rise while the real balance grows more slowly.

Compound interest warnings and boundaries
Condition	Boundary	Meaning
Zero horizon	Total months = 0	The schedule remains at the starting balance.
Target not reached	Ending balance < target balance	The gap row shows how far the selected plan misses the goal.
Negative real yield	Effective annual growth < inflation	Purchasing power shrinks under the assumptions.
Fee drag	Total fees > total interest	Charges consume more than the modeled interest gain.

Limitations:

The result is an educational projection, not financial advice. It does not account for changing market returns, variable tax rules, contribution limits, withdrawals, penalties, product terms, or investment losses.

Use the tax field as a simple reduction on credited interest, not a full tax calculation.
Use the inflation field as a planning assumption, not a forecast of future prices.
Compare real account and investment decisions with official product disclosures, tax guidance, account statements, and qualified advice.

Advanced Tips:

Compare +12 months ending with +1 pp rate ending before chasing a higher-rate assumption. Extra time can beat an optimistic rate change.
Use Rate Sweep when the rate is uncertain. A narrow band around the current rate shows how sensitive the plan is to assumption drift.
Check the no-fee scenario when Fees charged grows faster than expected. Small fixed monthly charges matter most on smaller balances.
Use Monthly Path to confirm deposit timing. Beginning contributions should appear before growth for that month; end contributions should appear after growth.
Keep inflation turned on when the target is meant to represent purchasing power, not just account dollars.
Use IRR (annualized) for contribution-heavy plans, because the nominal interest rate alone does not include the timing of cash you add later.

Worked Examples:

Ten-year savings plan

A $20,000 starting balance, $200 monthly contribution, 5% interest, monthly compounding, 10 years, end-of-month deposits, and 2.5% inflation produces an Ending balance near $63,997. The Ending balance (real) is near $49,994, so the real result is the better field for purchasing-power planning.

Target gap with costs included

A $10,000 start, $300 monthly contribution, 4% monthly-compounded rate, 8-year horizon, 15% tax on interest, 3% inflation, 1% annual fee, and $5 monthly fee finishes near $43,359 against a $50,000 target. The gap and fee rows show why the goal is not reached even though the account keeps growing.

Flat result warning

If Investment length is 0 years and 0 months, the schedule has no time to add deposits or interest. Increase the horizon, then confirm Monthly Path contains month-by-month rows and the zero-month warning is gone.

FAQ:

Why does compounding frequency change the result?

More frequent compounding credits interest sooner, so later periods can earn interest on a slightly larger balance. Annual, semiannual, quarterly, and monthly settings show scheduled crediting, while daily and continuous settings use a monthly-equivalent rate for the schedule.

Should I compare nominal or real ending balance?

Use Ending balance for account-dollar planning and Ending balance (real) for purchasing-power planning. A plan can look successful in nominal dollars while real growth stays thin.

What does IRR add when I already have an interest rate?

IRR (annualized) reflects deposit timing and final value. It can differ from the nominal rate when recurring contributions are large relative to the starting balance.

Why is my target not reached?

The target warning appears when the modeled ending balance stays below Target balance. Check the gap, then test a longer horizon, a higher contribution, lower fees, or a different rate assumption.

Does the tax rate field calculate my real tax bill?

No. Tax rate on interest is a simple percentage reduction on credited interest. It does not model filing status, deductions, tax-advantaged accounts, state rules, or when tax is actually due.

Glossary:

Nominal annual rate: The stated yearly rate before compounding frequency, tax, fees, or inflation adjustments.
Effective annual yield: The one-year growth rate after compounding frequency is applied.
Real annual yield: The effective annual yield after comparing modeled growth with inflation.
IRR: An annualized return measure that includes contribution timing and ending value.
Inflation drag: The difference between nominal ending balance and inflation-adjusted real balance.
Fee drag: The reduction caused by percentage account fees and fixed monthly fees.

References:

How does compound interest work?, Consumer Financial Protection Bureau, last reviewed October 19, 2023.
Compound Interest Calculator, Investor.gov, U.S. Securities and Exchange Commission.
Payment of interest, Consumer Financial Protection Bureau.
Topic no. 403, Interest received, Internal Revenue Service, updated April 10, 2026.
Consumer Price Index, U.S. Bureau of Labor Statistics.

Compound Interest Calculator

Projected Ending Balance

Current result

How to Use This Tool:

Interpreting Results:

Technical Details:

Formula Core:

Limitations:

Advanced Tips:

Worked Examples:

Ten-year savings plan

Target gap with costs included

Flat result warning

FAQ:

Glossary:

References:

Compound Interest Calculator

Projected Ending Balance

Current result

Introduction

How to Use This Tool:

Interpreting Results:

Technical Details:

Formula Core:

Limitations:

Advanced Tips:

Worked Examples:

Ten-year savings plan

Target gap with costs included

Flat result warning

FAQ:

Glossary:

References: