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
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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 interest is growth that keeps reusing its own past gains. Once interest is added back to the balance, later interest is earned on both the original money and the earlier interest, which is why time, contribution timing, and compounding frequency can matter almost as much as the stated rate.

That is also why long-horizon saving plans can surprise people. A steady monthly deposit can make the ending balance climb much faster than a lump sum alone, while taxes on interest, account fees, and inflation can quietly pull the outcome back down. Looking only at the final dollar total often hides those tradeoffs.

This calculator turns that problem into a fixed-assumption projection. It starts with an initial balance, adds recurring deposits, applies the selected compounding pattern, then adjusts the path for tax on credited interest, annual and monthly fees, and an inflation assumption. The result is a nominal ending balance, an inflation-adjusted balance, yield measures, target-progress timing, and schedules that show how the total was built over time.

It is best used for savings plans, deposit-account comparisons, and steady-growth what-if checks where you want to test assumptions rather than predict a volatile market. The projection is not a promise. If rates move, deposits change, fees differ, or tax treatment works another way in real life, the real outcome changes too.

Technical Details:

A nominal annual rate is only the starting point. The more often interest is credited, the sooner each gain starts earning on top of itself, which raises the effective annual growth. The calculator lets you compare annual, semiannual, quarterly, monthly, daily, and continuous compounding so you can see how that timing changes the result even when the nominal rate stays the same.

Recurring deposits change the path again. Money added earlier spends more time in the account, so beginning-of-period contributions grow more than end-of-period contributions. Frictions work in the opposite direction: tax on interest reduces each credited amount before it joins the balance, percentage fees skim the balance as it grows, and fixed monthly fees remove the same dollar amount no matter how small or large the account is.

Inflation answers a different question from compounding. The nominal ending balance tells you how many dollars the account may hold under the model. The real balance discounts that ending value into today's purchasing-power terms, which helps you judge whether the plan is merely growing in dollars or actually gaining ground after rising prices.

The same plan can look generous in nominal dollars but much thinner after fee drag, tax drag, and inflation are taken into account.

Formula Core

The projection uses one balance path for the whole term. Deposits can land before or after the month's growth, interest is credited according to the chosen compounding rule, and fees are removed after growth for that period.

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

Symbol mapping for the compound interest model
Symbol	Meaning	Plain-language reading
r	Nominal annual rate	The headline annual rate entered for the scenario
n	Compounding events per year	Annual, semiannual, quarterly, monthly, daily, or continuous growth timing
Dmpre / Dmpost	Deposit before or after growth	Contribution timing changes how long each deposit can compound
im	Monthly or event-period growth rate	The rate actually applied at that point in the schedule
t	Tax rate on credited interest	A flat haircut applied to each period's interest before it stays in the balance
Fm	Monthly fees	The combined percentage fee and fixed monthly fee removed from the account
pi	Inflation rate	The annual assumption used to convert the ending balance into today's purchasing power
M	Total months	The full length of the projection horizon

How each adjustment changes the projection
Adjustment	What it changes	What to watch
Contribution timing	Moves each recurring deposit before or after that month's growth and fees	Beginning timing usually lifts the ending balance because each deposit starts working sooner
Annual contribution growth	Raises the recurring deposit plan once per year	Useful when savings rise with salary or inflation
Tax on interest	Reduces each credited interest amount before it stays in the balance	Long horizons can lose more from repeated tax drag than the single rate entry suggests
Annual and monthly fees	Subtracts charges from the balance after growth	Small ongoing fees can compound into large long-term losses
Inflation adjustment	Changes only the real-balance reading, not the nominal path	A strong future dollar total can still represent weak purchasing-power growth

The calculator also estimates an annualized internal rate of return from the cash-flow pattern. That figure summarizes the whole deposit-and-ending-value path, so it is useful when recurring contributions matter. It is not the same thing as the nominal rate, and it may stay blank when the horizon is too short or the cash flows do not produce a usable annualized solution.

Everyday Use & Decision Guide:

Start with a plain baseline before adding frictions. Enter the starting balance, the nominal rate, the compounding choice, and the full horizon, then read whether the ending balance is being driven mostly by time, fresh deposits, or the quoted rate. That first pass keeps the main relationship visible before taxes, fees, and inflation complicate it.

Match recurring deposits to real life. If money lands at the start of the month, choose beginning timing. If it lands after the month's interest cycle, choose end timing.
Add the tax, fee, and inflation settings only when they apply to the plan you are testing. Those fields are best used to pressure-test a scenario, not to guess details you do not know.
Set a target balance when the real question is timing. A reach date or remaining gap is often more useful than the final balance alone.
Use the built-in comparisons to see whether lower fees, one extra year, or a 1-point rate change has the biggest effect on the outcome.

Snapshot is the quickest read because it combines summary metrics, an action guide, and side-by-side scenario lifts. Milestone Runway and Growth Runway are better when you care about timing and target progress. Annual Path and Monthly Path help when you need to see how the total is changing period by period rather than only at the finish.

Balance Mix is the fastest way to see how much of the ending figure came from initial capital, recurring deposits, and compounded gain. Rate Sweep reruns the same scenario from 2 percentage points below the chosen nominal rate to 2 points above it, which is useful when the plan looks attractive only if the rate assumption stays unusually favorable.

Step-by-Step Guide:

Enter Initial investment, Interest rate, Compound frequency, and Length to define the base scenario.
Add Monthly contribution and Annual contribution if the plan includes fresh money. Then choose Contribution timing so deposits land when they actually would.
If the savings plan is expected to step up over time, enter Annual contribution growth. In this calculator, that yearly increase applies to the recurring deposit plan used in the schedule.
Use Tax rate on interest, Inflation rate, Annual fee, Monthly fee, and Target balance only when you want those assumptions included in the model.
Read the top summary and the Snapshot tab first. Then open Milestone Runway, Growth Runway, and Rate Sweep if you need timing, sensitivity, or target context.
If Monthly Path is empty or IRR (annualized) stays blank, check Length first. A horizon of 0 months leaves no schedule to annualize.

Interpreting Results:

Ending balance is the modeled dollar total at the end of the horizon. Ending balance (real) asks what that total is worth after adjusting for the inflation assumption. If those two values drift far apart, the plan may be growing in dollars while barely improving purchasing power.

How to read major outputs in the compound interest calculator
Output	What it answers	Common misread
Ending balance	How many dollars the account may hold under the chosen assumptions	It does not tell you what those dollars may buy later
Ending balance (real)	What the modeled ending balance is worth in today's purchasing power	It is not a prediction of actual future inflation
Effective annual yield	The annual growth implied by the nominal rate and compounding frequency	It does not include fee drag or inflation drag
IRR (annualized)	The annualized result of the modeled cash flows	It is not just the stated interest rate restated in a different format
Goal status	Whether the target is reached and, if so, how long it takes	It is not a guarantee that the target will be reached in real life

Three boundaries matter most. If Real annual yield is below 0%, the scenario is losing purchasing power. If Fees charged are greater than Compounded gain, the account costs are doing more damage than the modeled growth is helping. If Goal status shows a gap instead of a reach date, the current mix of rate, deposits, and horizon does not get to the target on time.

The main false-confidence trap is treating a large nominal ending balance as a complete answer. A better check is to compare the current plan with the built-in no-fee, +1 percentage point, and +12 month scenarios, then inspect Monthly Path or Milestone Runway to confirm the balance is moving the way you expect.

Worked Examples:

Regular monthly saving over ten years

Start with $10,000, add $250 at the end of each month, use a 5% nominal rate with Monthly compounding, and run the plan for 10 years. The calculator projects an Ending balance of $55,290.66. Of that total, $40,000.00 is contributed capital and $15,290.66 is compounded gain. The result shows a common savings pattern: fresh deposits still do most of the heavy lifting, but compounding becomes meaningful because the deposit base keeps growing.

A strong nominal total can still feel much smaller after costs and inflation

Use $15,000 as the starting balance, add $300 each month, set the nominal rate to 6% with Monthly compounding, and project 15 years. Then add 3% inflation, a 1% annual fee, a $5 monthly fee, and a $100,000 target. The nominal ending balance reaches $110,499.21, but the real balance is only $70,925.24 and total fees reach $9,430.77. The target is reached after 166 months, which is about 13 years 10 months. This is exactly the kind of case where the real balance and fee totals matter more than the headline finish.

Troubleshooting an empty schedule

Suppose you enter $10,000, a 5% nominal rate, Monthly compounding, and a Length of 0 years 0 months. The projected ending balance stays at $10,000.00, but the annual and monthly schedules are empty and IRR (annualized) stays blank because there is no time span to analyze. Change the horizon to 1 year and the same balance grows to $10,511.62, which restores the schedule and gives the model enough runway to report an annualized return.

FAQ:

Why can IRR be blank even when the ending balance is shown?

The ending balance only needs a completed projection path. IRR (annualized) needs a usable time-based cash-flow solution. A horizon of 0 months, or some cash-flow patterns, can leave the ending balance visible while the IRR field stays empty.

Why does daily or continuous compounding still show one row per month?

The calculator keeps its schedules on a monthly timeline so deposit timing, fees, milestones, and annual checkpoints remain easy to compare. Daily and continuous settings are translated into an equivalent monthly growth path for those tables and charts.

Does the tax setting represent my real tax bill?

No. The tax field is a flat reduction applied to each credited interest amount inside the model. Real tax treatment can differ by account type, country, timing, and other rules, so use it as an estimate rather than a formal tax calculation.

What is the difference between effective annual yield and real annual yield?

Effective annual yield reflects the stated nominal rate plus the chosen compounding frequency. Real annual yield goes one step further and adjusts that growth for the inflation assumption, so it is closer to a purchasing-power reading.

Does it keep my balances local?

Yes. The projection, schedules, comparisons, and chart data are calculated in your browser rather than being sent to a calculation service.

Glossary:

Nominal rate: The stated annual rate before compounding frequency, taxes, fees, or inflation are considered.
Effective annual yield: The annual growth implied by the nominal rate and the selected compounding pattern.
Real balance: The ending balance translated into today's purchasing-power terms using the inflation assumption.
IRR: Internal rate of return, an annualized measure based on the modeled timing of money going in and the ending value coming out.
Contribution timing: Whether each recurring deposit enters before or after that month's growth and fees are applied.

References:

What is compound interest?, Investor.gov.
12 CFR 1030.2 - Definitions, Consumer Financial Protection Bureau.
12 CFR 1030.7 - Payment of interest, Consumer Financial Protection Bureau.
CPI Questions and Answers, U.S. Bureau of Labor Statistics.
How Fees and Expenses Affect Your Investment Portfolio, Investor.gov.