Model how a starting balance and fixed monthly deposits could change under a constant hypothetical annual rate. Separate contributions from modeled growth, compare lower and higher rate cases, and inspect a year-by-year projection without treating the result as a forecast.
Mortgage & Loans calculator Content updated 2026-08-16Calculations run privately in your browser
Cindy Zhang and Heather Kincaid co-authored the plain-language explanation of the constant-rate compound-growth model, contribution timing, worked arithmetic, year-by-year interpretation, limitations, and links to the cited Investor.gov resources. This is an editorial authorship scope, not a claim of investment, securities, fiduciary, tax, legal, financial-planning, or other professional review.
The byline does not claim professional credentials, trade, finance, insurance, actuarial, underwriting, or claims experience, licensed review, or independent professional review for either author.
Enter growth assumptions
Example values are prefilled
How to use this compound interest calculator
Project compound growth from a starting balance, recurring monthly contributions, annual rate, time horizon, compounding frequency, and deposit timing.
Formula
Monthly-equivalent rate q = (1 + j ÷ m)^(m ÷ 12) − 1, where j is the nominal annual rate and m is compounds per year. With N months and end deposits C, FV = P(1 + q)^N + C[(1 + q)^N − 1] ÷ q; beginning deposits multiply the contribution term by (1 + q), with a separate q = 0 case.
Quick example
Example: A $10,000 starting balance plus $500 at each month-end for 20 years at a hypothetical nominal 7% compounded monthly grows to approximately $300,851. Of that amount, $130,000 is contributed principal and about $170,851 is modeled growth before taxes and fees.
Accuracy and limitations
This is deterministic arithmetic, not a return forecast. Real investment returns vary and can be negative; sequence, volatility, fees, taxes, inflation, contribution changes, withdrawals, and account rules can materially alter outcomes. Nonmonthly compounding is converted to an equivalent monthly factor for the fixed monthly cash-flow model, and daily compounding does not reproduce an institution's day-count, accrual, or crediting rules.
Sources and formula references
Investor.gov: Compound Interest Calculator — SEC investor-education reference for initial investment, monthly contribution, time, estimated annual rate, rate variance, and compounding frequency
Investor.gov: Understanding Fees — SEC investor education explaining how fees reduce the money that remains invested and can materially affect long-horizon outcomes
Investor.gov: What Is Risk? — SEC investor education on uncertainty, potential loss, volatility, inflation, liquidity, and differences among saving and investment products
Choose and verify your inputs
Record one starting balance
Use the balance available at the beginning of the selected period and date the figure in saved notes. Keep future deposits out of this field so the result can distinguish contributed principal from modeled growth.
Choose a sustainable deposit assumption
Enter a fixed monthly amount only when that pattern matches the scenario you want to examine. The calculator does not model skipped deposits, annual contribution increases, employer matches, limits, withdrawals, or changing cash flow.
Distinguish nominal rate from effective yield
Enter a hypothetical nominal annual rate paired with its stated compounding frequency. APY or effective annual yield already incorporates compounding and should not be entered as nominal without conversion; when costs apply, a lower net-of-fee scenario is more informative than ignoring them.
Match timing and horizon
Select whether recurring deposits occur at the beginning or end of each month and enter the full modeled years. Deposit timing changes how long each contribution grows, while a longer horizon magnifies both rate assumptions and input errors.
Use scenarios, not a promised return
Treat the lower, entered, and higher rates as mathematical cases. Investor.gov notes that investments involve uncertainty and potential loss, so no single constant rate represents the path an investment account will actually follow.
How the calculation works
Convert the stated compounding convention
Divide the nominal annual rate by the selected number of compounding periods, then derive an equivalent monthly growth factor so the model can place monthly deposits on one consistent time line.
Grow the opening balance
Carry the current balance through each modeled month using the equivalent monthly factor. At a 7% nominal rate compounded monthly, the monthly factor is 0.07 ÷ 12, while other selected frequencies produce a mathematically equivalent monthly factor.
Place each recurring deposit
For beginning-of-month timing, add the contribution before that month's growth. For end-of-month timing, apply growth first and then add the contribution, so every beginning deposit receives one additional modeled month compared with an otherwise identical end deposit.
Separate deposits from modeled growth
Add the starting principal to every scheduled monthly contribution to calculate total contributed principal. Subtract that amount from the ending balance to report modeled growth, which can be negative in a negative-rate scenario.
Create year and rate comparisons
Capture contributed principal, cumulative modeled growth, and ending balance at each year-end, then repeat the full projection at rates two percentage points below and above the entered case. These are sensitivity calculations, not probability bounds.
Worked calculation: Consider $10,000 available at the start, a $500 deposit at the end of every month, 20 full years, and a hypothetical nominal 7% annual rate compounded monthly, with taxes and fees excluded.
Convert the nominal rate to a monthly rate: 0.07 ÷ 12 = 0.00583333, or about 0.583333% per month, across 240 modeled months.
The $10,000 opening principal grows by (1 + 0.07 ÷ 12)^240 to approximately $40,387.39 under the constant-rate assumption.
The 240 end-of-month deposits use the ordinary-annuity factor: $500 × {[(1 + 0.07 ÷ 12)^240 − 1] ÷ (0.07 ÷ 12)} ≈ $260,463.33.
Add $40,387.39 and $260,463.33 to obtain an ending balance of approximately $300,850.72, displayed as about $300,851.
The starting $10,000 plus $120,000 of deposits equals $130,000 contributed. Subtracting that from $300,850.72 leaves approximately $170,850.72 of modeled growth before fees and taxes.
Result: The corrected example produces about $300,851, not $283,000. The year-by-year table is a smooth deterministic path built from one constant rate; an actual saving or investment account can credit interest differently, charge fees, fluctuate, lose value, receive uneven deposits, or be affected by taxes and withdrawals.
Next step: Repeat the case at lower rates, subtract relevant ongoing costs from the assumed return when appropriate, compare the result with current product disclosures or account statements, and keep the output labeled as a hypothetical projection rather than a forecast.
Interpret the result
Ending balance
This is the result of applying one constant rate and one fixed deposit pattern for the full horizon. It is not an account statement, market forecast, insured value, or guarantee and should be labeled with the assumptions whenever it is saved or shared.
Contributed principal and growth
Total contributed is the starting balance plus scheduled deposits; modeled growth is the mathematical difference between that amount and the ending balance. Growth is not the same as realized after-tax investment return and can be negative under a loss scenario.
Effective annual yield
The effective annual figure translates the entered nominal rate and selected frequency into one annualized compounding result. Use it to understand this model's rate convention, not as a substitute for an institution's disclosed APY, investment return, or fee schedule.
Year-by-year projection
The table shows how the compounding assumption accumulates over time and helps reveal when contributions versus modeled growth drive the balance. Smooth annual rows conceal the volatility and sequence effects that occur in real markets.
Lower and higher rate cases
The sensitivity cases show how strongly a long projection reacts to a two-percentage-point rate change. They are not best- and worst-case guarantees; losses, fees, taxes, inflation, and cash-flow changes can produce results outside that range.
Common mistakes to avoid
Entering an advertised APY or effective annual return as a nominal rate without matching the compounding convention.
Treating a constant historical or hypothetical return as a guaranteed future path.
Ignoring fees, expenses, taxes, and inflation even though each can materially reduce usable growth over a long horizon.
Choosing beginning-of-month deposits when contributions actually arrive after the period, or counting the same starting money again as a monthly deposit.
Comparing two products only by nominal rate when their compounding, liquidity, insurance, risk, fees, and tax treatment differ.
Using a smooth compound-growth projection as a debt-payoff schedule even though this tool does not model loan payments, finance charges, or lender allocation rules.
Decision checklist
Write down whether the source rate is nominal, APY, guaranteed for a period, or merely hypothetical, and match the compounding frequency.
Run lower, entered, and higher rate cases and label each saved result with its rate, timing, deposit, horizon, and calculation date.
Review product and account disclosures for transaction fees, ongoing expenses, withdrawal charges, contribution limits, taxes, and liquidity restrictions.
Compare the projection with an explicit zero-growth case so the effect of contributions is visible without assumed returns.
Update the starting balance and contribution pattern when circumstances change rather than preserving an outdated long-range result.
Use appropriately qualified financial, tax, or legal guidance when choosing products or making material decisions; the calculator supplies arithmetic only.
Frequently asked questions
Why does contribution timing matter?
A beginning-of-month deposit receives approximately one additional month of modeled growth compared with an end-of-month deposit.
Is a higher compounding frequency always much better?
At the same nominal rate it increases effective yield, but the difference is often smaller than fees, taxes, contribution changes, or return uncertainty.
Can the rate be negative?
Yes. A negative constant rate can illustrate a mathematical loss scenario, though real returns fluctuate rather than following a smooth path and may produce outcomes outside the displayed sensitivity range.
Should I enter APY or a nominal annual rate?
Enter a nominal annual rate paired with its compounding frequency. APY already incorporates compounding and should not be entered as nominal without conversion; verify the definition in the product disclosure.
Does the result include investment fees or taxes?
No. Use a reasonable net-of-fee rate when appropriate and evaluate taxes separately. Investor.gov explains that even seemingly small fees can have a major long-term effect because less money remains invested to earn a return.
Why will an actual account differ from this projection?
Real returns change over time, deposits may vary, and institutions use specific accrual, crediting, day-count, fee, tax, and withdrawal rules. Investments also involve uncertainty and potential loss.
Can I use this as a loan-payoff calculator?
No. This tool models a nonnegative starting balance plus deposits. It does not model required loan payments, daily interest, fees, delinquency, or lender allocation rules; use the mortgage or auto-loan calculator for those defined fixed-rate scenarios.
Does the projection account for inflation?
No. The ending balance is stated in future nominal dollars under the entered rate. Compare purchasing power separately using an inflation assumption appropriate to the planning question.
