Compound Interest Calculator

Projected Ending Balance

$ {{ money(projection.endingBalance) }}

Real balance: $ {{ money(projection.endingBalanceReal) }} · {{ projection.goalStatusText }}

APY {{ percentDisplay(projection.effectiveAnnualYield, 2) }} Real {{ percentDisplay(projection.realAnnualYield, 2) }} Double {{ projection.doublingTimeLabel }} Interest {{ projection.interestShareLabel }} {{ projection.goalBadgeLabel }}

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.

Metric	Value	Copy
{{ row.label }}	{{ row.display }}
Action guide: {{ row.action }}	{{ row.priority }} {{ row.why }}
Fast comparison: {{ row.label }}	Ending {{ money(row.ending) }}; lift {{ signedMoney(row.lift) }}
Warning {{ index + 1 }}	{{ warning }}

Checkpoint	Invested ($)	Ending ($)	Real ($)	Goal progress	Copy
{{ row.label }}	{{ money(row.invested) }}	{{ money(row.ending) }}	{{ money(row.realEnding) }}	{{ row.goalProgressDisplay }}

Year	Invested ($)	Interest ($)	Fees ($)	Real ($)	Ending ($)	Copy
{{ row.label }}	{{ money(row.invested) }}	{{ money(row.interestCum) }}	{{ money(row.feesCum) }}	{{ money(row.realEnding) }}	{{ money(row.ending) }}

Month	Deposit ($)	Interest ($)	Fees ($)	Ending ($)	Copy
{{ row.label }}	{{ money(row.deposit) }}	{{ money(row.interest) }}	{{ money(row.fee) }}	{{ money(row.ending) }}

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Compound growth becomes noticeable when interest is left in the account long enough to earn more interest. A savings account, certificate of deposit, bond estimate, or long-term investing plan can start with the same dollar amount and the same stated rate, then finish in different places because interest is credited on different schedules and new deposits arrive at different times.

The first number people usually notice is the future balance, but the balance alone does not explain the plan. Principal is the money already there. Contributions are the new deposits added along the way. The nominal annual rate is the stated yearly rate before compounding frequency changes its effect. The effective annual yield shows the one-year growth after compounding has been applied, and the real balance discounts future dollars for inflation.

Time: Longer horizons give each interest credit more chances to become part of the next interest calculation.
Deposit pattern: Earlier and steadier deposits usually compound more than late deposits of the same total amount.
Costs and taxes: A tax haircut on interest, a percentage account fee, or a fixed monthly charge can reduce the amount that stays invested.
Inflation: A larger nominal balance can still buy less than expected if prices rise faster than the account grows.

Compound interest flow from principal and deposits through compounding, costs, and real balance adjustment

A common mistake is to compare only the stated annual rate. Monthly compounding at a given rate earns a little more than annual compounding at the same stated rate, while a fee or tax applied every period can erase part of that advantage. Contribution timing matters too, because a deposit made before a crediting period starts earning sooner than a deposit made afterward.

Compound-interest projections are planning models, not promises. They work best when the rate, deposit pattern, tax treatment, fees, and inflation assumption are stable enough to compare scenarios. Real accounts and investments may change rates, limit deposits, charge penalties, or expose the balance to market gains and losses that a fixed-rate projection cannot settle.

How to Use This Tool:

Start with the assumptions you can defend, then use the comparison rows and warnings to pressure-test the plan.

Enter Initial investment and Monthly contribution. Use the recurring contribution fields for money you expect to add steadily, not one-time windfalls.
Set the nominal Interest rate and Compound frequency. The frequency changes the effective annual yield even when the rate entry stays the same.
Enter Investment years and months. A zero-month horizon keeps the result at the starting balance and triggers a warning.
Use Target balance when you want a goal badge, goal status, and runway rows. The target changes the interpretation, not the balance math.
Open Advanced for annual contributions, beginning-or-end contribution timing, contribution growth, tax on interest, inflation, percentage fees, and fixed monthly fees.
Review Projection Snapshot first, then check Milestone Runway, Annual Path, Monthly Path, Balance Mix, Growth Runway, and Rate Sweep when you need the schedule or sensitivity detail.

If a warning says the target is not reached, fees exceed interest, or inflation beats modeled growth, change one assumption at a time and compare the new snapshot against the original.

Interpreting Results:

The 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 judging purchasing power. Total invested capital, Recurring contributions, Compounded gain, and Fees charged explain how the final balance was built.

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

Do not treat a high nominal ending balance as a promise or a sufficient retirement answer. Verify the real balance, the warning rows, and the monthly or annual schedule before relying on the result for a financial decision.

Technical Details:

The nominal annual rate is first converted into an effective annual yield. Annual, semiannual, quarterly, and monthly compounding use scheduled crediting events. Daily compounding is represented as an equivalent monthly growth rate for the monthly path, and continuous compounding uses the exponential limit. That distinction keeps the annual yield consistent while still showing a readable month-by-month schedule.

Recurring deposits are spread across the monthly path. Beginning-of-month deposits join the balance before that month's growth; end-of-month deposits join after any growth and fees. Tax on interest is applied to each credited interest amount before it compounds into later balances. The percentage account fee is divided across months, the fixed monthly fee is added to that deduction, and the monthly fee charge cannot reduce the balance below zero. Real balances divide nominal balances by the inflation factor for the elapsed time.

Formula Core:

The core equations show how the rate is converted and how the balance advances through each modeled month. In the monthly recurrence, im is zero in months with no scheduled interest credit for annual, semiannual, and quarterly settings.

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}}}

Compound interest symbol map
Symbol	Meaning	Related input or output
r	Nominal annual rate as a decimal	Interest rate
n	Compounding events per year	Compound frequency
im	Scheduled monthly credit rate, event-period rate, or zero when no credit is due	Monthly equivalent rate and schedule interest
Dpre, Dpost	Deposit before or after monthly growth	Contribution timing
t	Tax rate applied to credited interest	Tax rate on interest
Fm	Monthly percentage and fixed fee deduction, capped at the current balance	Annual fee and monthly fee
pi	Annual inflation assumption	Inflation rate and ending balance (real)

A 5% nominal rate compounded monthly has an effective annual yield of about 5.116%. With a 2.5% inflation assumption, the real annual yield is about 2.553% before taxes and fees. That gap explains why the real balance can trail the nominal balance even when every monthly row is growing.

Warnings and interpretation boundaries
Condition	Boundary	Meaning
Zero horizon	Total months = 0	The schedule stays at the starting balance.
Target not reached	Ending balance < target balance	The gap row shows how much 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. It does not account for changing market returns, variable tax rules, account contribution limits, withdrawal timing, bank product terms, or investment risk.

The calculation runs from the values you enter in the browser. It is not connected to a bank, brokerage, tax account, or live inflation feed, so official statements and current product disclosures remain the source of truth.

Use the tax field only as a simple haircut on credited interest.
Use the inflation field as a planning assumption, not a forecast.
For real investments, compare the result with official account statements, product disclosures, and qualified financial advice.

Worked Examples:

Ten-year savings plan

A starting balance of $20,000, a $200 monthly contribution, 5% interest, monthly compounding, 10 years, and 2.5% inflation produces an Ending balance near $65,000 before any optional tax or fee drag. The Ending balance (real) is lower because future dollars are discounted back to today's purchasing power.

Goal gap under a short horizon

Keeping the same rate but setting a $100,000 Target balance over only 10 years leaves the Goal status as not reached. The useful next check is +12 months ending versus +1 pp rate ending, because those rows show whether time or rate sensitivity matters more.

Troubleshooting a flat result

If Investment years and months are both zero, the schedule has no time to add deposits or interest. Increase the horizon, then confirm that Monthly Path contains month-by-month rows and that warnings no longer report a zero-month projection.

FAQ:

Why does compounding frequency change the result?

More frequent compounding credits interest sooner, so later periods earn interest on a slightly larger balance. Annual, semiannual, quarterly, and monthly settings show their scheduled crediting pattern, 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 the timing of deposits and the 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.

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 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.

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.
Topic no. 403, Interest received, Internal Revenue Service.
Consumer Price Index, U.S. Bureau of Labor Statistics.