Inputs and Outputs of the Compound Interest Simulator
This simulator is a mathematical projection tool designed to estimate asset growth when investing regular monthly contributions at a fixed hypothetical annual interest rate.
In the "Investment & Management Settings" panel, you configure four parameters: Initial Investment, Monthly Contribution, Expected Annual Return, and Investment Period.
The default configuration sets an initial investment of 1,000,000 yen, a monthly contribution of 30,000 yen, an assumed annual return of 5%, and an investment span of 20 years.
"Initial Investment" represents the starting balance at the beginning of the investment period. Setting this to 0 yen simulates accumulation built solely through monthly contributions.
"Monthly Contribution" is the fixed sum deposited at the end of each month; setting it to 0 yen evaluates the growth of the initial principal alone.
"Expected Annual Return" is the annual rate used internally to calculate monthly compounding. "Investment Period" is specified in years, accepting values between 1 and 50 years via numeric input.
Adjusting any input recalculates final accumulated principal, total compound assets, projected compound investment gains, and the difference relative to a reference simple interest model.
Directly below the controls, an interactive chart presents yearly progression using stacked bars and a dashed comparison line, accompanied by a detailed table breaking down principal, compound assets, simple interest figures, and model differences for each year.
This page evaluates a simplified mathematical model assuming uniform monthly deposits and an unvarying annual return across the entire span.
It is not designed to select specific financial instruments or forecast future market performance. Use these projections primarily to understand the mechanics of compound interest and interpret what the displayed figures represent.
Converting Annual Return to Monthly Rates
The tool converts the entered annual percentage into a decimal by dividing by 100, and then divides that value by 12 to establish the monthly rate.
Letting i represent the annual rate and r represent the monthly rate, the internal formula is r = i ÷ 100 ÷ 12. For an annual rate of 5%, the monthly applied rate is 0.05 ÷ 12, or approximately 0.0041667 (roughly 0.4167% per month).
A distinction must be made between the entered 5% annual figure and the effective annual growth resulting from monthly compounding.
Applying a monthly rate of 0.4167% twelve times to a fixed principal without withdrawals or deposits yields an annual increase of (1 + 0.05 ÷ 12)^12 − 1, which is approximately 5.1162%.
The 5% figure entered here is not a promise of an exact 5.0% annual increase, but a computational parameter applied in twelve equal monthly increments.
Savings accounts, mutual funds, and insurance products use differing yield definitions, compounding intervals, business day conventions, day-count fractions, fee deductions, and rounding rules.
Consequently, a real-world product labeled with a 5% annual return will rarely match the output of this tool exactly. The annual rate here serves strictly as a standardized modeling parameter rather than an asset's quoted yield or historical return.
Calculation Sequence for End-of-Month Contributions
Whether contributions occur at the beginning or end of each month alters how many compounding cycles each deposit receives. This simulator utilizes an end-of-month contribution schedule.
Each month, the monthly interest rate is applied to the beginning balance first, after which the monthly contribution is added. Letting B represent the beginning balance, r the monthly rate, and PMT the monthly contribution, the balance carried into the next month is B × (1 + r) + PMT.
Under this sequence, newly deposited contributions at the end of the month earn no interest during that initial month. The first deposit begins compounding in the second month, while the final contribution made in the last month earns no interest before the simulation ends.
An annuity-due model depositing funds at the beginning of each month would allow each payment to compound for an extra month, producing higher final values under identical parameters.
For an initial principal P and total months N, the monthly iterative loop matches the standard future-value formula for ordinary annuities when the rate is non-zero: P × (1 + r)^N + PMT × ((1 + r)^N − 1) ÷ r.
Rather than evaluating this formula in a single equation, the tool iterates through N monthly cycles sequentially, recording the balance at every 12-month interval.
Deposit schedules vary across financial institutions, where non-trading days and settlement delays can influence actual balances.
This tool does not accommodate custom deposit dates, daily compounding, or switches between beginning-of-month and end-of-month deposits.
Read the "Monthly Contribution" parameter as a fixed sum added immediately after each month's interest is credited.
Example Breakdown of Principal, Compound, and Simple Interest
Accumulated principal represents the initial investment plus all monthly contributions made up to that point. With an initial investment of 1,000,000 yen, monthly deposits of 30,000 yen, and a 20-year horizon (240 months), the total principal is 1,000,000 yen + (30,000 yen × 240), which equals 8,200,000 yen.
Under these same conditions at a 5% annual return, monthly compounding with end-of-month deposits produces a total compound asset balance of 15,043,650 yen at year 20.
"Projected Compound Investment Gain" is calculated by subtracting accumulated principal from the rounded total compound assets, yielding a gain of 6,843,650 yen.
The comparative simple interest model applies Initial Investment × (1 + Annual Rate × Elapsed Years) to the starting capital. For monthly deposits, simple interest is applied to each payment only for the remaining months after it was made.
The first deposit receives 239 months of simple interest, the second receives 238 months, and the final deposit receives 0 months.
Under this model, the 20-year balance is 12,785,000 yen, resulting in a difference of 2,258,650 yen compared to the compound interest balance.
This difference illustrates the numerical variance between this specific monthly compounding model and an identical rate evaluated under linear simple interest.
It does not represent a universal compound growth figure applicable to all asset classes. Equities and investment trusts fluctuate in price and do not yield steady monthly interest payments, nor does this calculation replicate cash flows from commercial simple-interest or distribution-focused investment products.
Reading Charts, Annual Tables, and Yen Rounding
On the asset growth chart, stacked bars represent the compound interest model. The gray section indicates accumulated principal, the green section represents projected compound gains, and the top of each bar indicates total compound assets.
The dashed line depicts the comparative simple interest model. Hovering your mouse cursor over any year displays the principal, compound assets, compound gains, simple model assets, and simple model gains for that year.
The annual breakdown table displays exact numerical figures at the close of each year. By default, it presents the first five years, and clicking "Show Full Period" expands the entire schedule for your selected investment span.
This allows you to track how principal and both interest models diverge year by year from the first year onward.
Internally, compound balances retain fractional yen values across monthly steps. When generating display figures at each 12-month interval, Math.round rounds the compound and simple interest totals to the nearest whole yen.
The rounded values shown on screen are not fed back into the internal simulation state for subsequent months.
Consequently, the displayed annual values do not reflect accounts where interest is truncated or settled to the exact yen each month.
Real-world financial products apply distinct rounding, taxation, and fee conventions to interest, distributions, unit shares, and currency conversions.
The whole-yen numbers in the table are estimates derived from monthly floating-point iteration and display rounding.
Simulation Limitations and Operational Notices
This tool operates on the premise that the entered annual interest rate remains completely unchanged throughout the investment horizon.
In reality, market assets such as stocks and mutual funds fluctuate with economic conditions and may drop below invested capital.
Because annual market volatility, down years, and recovery sequences are replaced by an unvarying return, this tool does not forecast actual market trends or investment returns.
Taxes, brokerage commissions, account maintenance fees, trust fees, dividend distributions, reinvestment conditions, currency exchange fluctuations, and inflation-driven purchasing power loss are not included in calculations.
It does not model Japan's tax-exempt NISA system, annual or lifetime contribution allowances, or account categories. Dynamic cash flow changes—such as altering contribution amounts mid-stream, suspending deposits, making partial withdrawals, or adding lump-sum investments—are likewise unsupported.
Furthermore, the tool does not provide target-sum goal-seeking, Rule of 72 doubling calculations, pre-tax versus post-tax comparisons, risk tolerance profiling, historical market forecasting, Monte Carlo simulations, or CSV/PDF exports.
Its functionality is strictly confined to forward mathematical calculations of principal and two static interest models based on the four user inputs.
Displayed final balances do not guarantee future returns or capital preservation. They do not constitute financial recommendations, solicitation, or personal investment advice.
Review current documentation from product providers regarding fees, taxation, terms, and investment risks, and make all investment decisions independently.