Compound interest vs simple interest investment return comparison simulator | ZeroTools

The "Compound vs. Simple Interest Investment Return Comparison Simulator" is a tool that compares asset trajectories under two mathematical models when a constant assumed annual yield continues for an initial investment and monthly fixed contributions.

It computes under identical conditions both a compound interest model, which includes accrued interest in subsequent interest calculations, and a comparison simple interest model, which calculates interest solely on contributed principal.

It does not select actual financial products or forecast future market performance.

The tool accepts four inputs: initial investment amount, monthly contribution amount, assumed annual yield, and investment period.

Initial investment and monthly contribution amounts are specified in units of 10,000 JPY. The default values are 1,000,000 JPY initial investment, 30,000 JPY monthly, 5% annual yield, and a 20-year horizon.

Setting the initial investment to 0 JPY models monthly contributions only, while setting monthly contributions to 0 JPY models lump-sum investing with initial funds alone.

Input sliders support 0 to 10,000,000 JPY for initial investment, 0 to 500,000 JPY for monthly contributions, 0% to 15% for annual yield, and 1 to 40 years for duration.

Annual yield can also be typed directly into the numeric field within a range of 0% to 30%. Modifying any input recalculates the SVG line chart on the right, the final-year compound and simple totals, the difference between them, and the annual comparison table under the same conditions.

The purpose of this page is not to state definitively how much profit compound interest will produce, but to observe how constant-rate model figures diverge depending on whether past interest is added to subsequent interest calculations.

Displayed figures do not represent specific product yields, future amounts received, or guaranteed principal.

In the compound interest model, the entered annual rate is divided by 100 and then divided by 12 to yield the monthly rate. Letting i denote the annual rate and r denote the monthly rate, the internal relationship is r = i ÷ 100 ÷ 12.

For an annual rate of 5%, the monthly applied rate is 0.05 ÷ 12, or approximately 0.4167% per month.

The calculation sequence for each month first applies the monthly rate to the balance carried over from the prior month, and then adds that month's contribution.

If B is the opening balance and PMT is the monthly contribution, the balance carried forward to the following month is B × (1 + r) + PMT.

Consequently, new capital added at the end of the month earns no interest in that same month and becomes subject to interest starting the following month.

Under this end-of-month contribution model, the first contribution earns interest for N − 1 months until the end of the term, while the final contribution earns interest for 0 months.

When an initial principal with no intermediate deposits or withdrawals is compounded monthly over 12 months at an annual rate of 5%, the one-year increase is (1 + 0.05 ÷ 12)^12 − 1, or approximately 5.1162%.

An entered yield of 5% does not mean principal grows by exactly 5.0000% over one year, but represents the condition of applying a monthly rate equal to 5% divided into 12 equal parts.

Actual savings deposits, mutual funds, and insurance contracts differ in annual rate definitions, interest and dividend distribution frequencies, business days, day-count conventions, fees, and rounding rules.

This tool does not support switching to start-of-month contributions, arbitrary contribution dates, daily compounding, or variable monthly contribution amounts.

Nor does it replicate the price volatility of dollar-cost averaging where purchased unit volumes vary with market prices.

The simple interest model uses the same entered annual rate, monthly rate, and end-of-month contribution conditions as the compound model.

The difference is that interest accumulated in past months is never included in subsequent monthly interest calculations. Each month's interest is calculated solely on the principal contributed up to that calculation timing.

Because each month's contribution is added after that month's interest calculation, it is not eligible for interest in that initial month.

Where P is the initial investment and N is the number of months, the initial investment portion is P × (1 + rN). The cumulative principal of monthly contributions is PMT × N, and the total simple interest accrued across all contributions according to their respective remaining months is PMT × r × N(N − 1) ÷ 2.

Therefore, the final value of the comparison simple interest model is the sum of these three components. It sums the return where the first contribution earns N − 1 months of interest, the second earns N − 2 months, and the final contribution earns 0 months of interest.

While the interface displays the simple interest model balance inclusive of accrued interest, it does not move interest into a separate cash account or simulate physical withdrawals.

"Simple interest" here serves purely as a computational baseline in which interest itself is not incorporated into the principal for subsequent interest calculations.

It does not replicate payout mechanisms of specific financial products such as time deposits or bonds.

With only an initial investment and no ongoing contributions, simple interest grows along a constant linear slope over time. However, when regular monthly contributions are added, each addition has a different remaining term, introducing an N(N − 1) quadratic term into the formula.

As a result, the simple interest model trajectory on the line chart cannot be assumed to be a straight line.

The "Difference" in the dashboard and annual comparison table is obtained by subtracting the simple interest model value from the compound interest model value.

It represents a neutral comparative metric of "Compound − Simple" rather than an indicator of relative superiority or investment success between financial products.

At an annual rate of 0%, both models match cumulative invested principal exactly. If initial investment and monthly contributions are both 0, both models yield 0 JPY regardless of the annual rate.

Examining the default inputs of 1,000,000 JPY initial investment, 30,000 JPY monthly, 5% annual rate, and 20 years illustrates the progression.

Total invested principal over 20 years is 8,200,000 JPY (1,000,000 JPY plus 30,000 JPY × 240 months). The end-of-month compound interest model reaches 15,043,650 JPY, the comparative simple interest model under identical end-of-month timing reaches 12,785,000 JPY, and the displayed difference is 2,258,650 JPY.

Under the same conditions at Year 1, against invested principal of 1,360,000 JPY, the compound model is 1,419,528 JPY, the simple model is 1,418,250 JPY, and the difference is 1,278 JPY.

At Year 5, compound is 3,323,541 JPY, simple is 3,271,250 JPY, and difference is 52,291 JPY. At Year 10, compound is 6,305,478 JPY, simple is 5,992,500 JPY, and difference is 312,978 JPY.

While the divergence grows over longer horizons, it can be relatively modest at lower interest rates or shorter durations.

For non-negative contributions and annual yields of 0% or higher accepted by this tool, the compounded value for identical contributions is always greater than or equal to the corresponding simple interest value.

However, this holds under the internal constraints of a constant non-negative interest rate. It cannot be directly extrapolated to real-world investments involving price declines, negative rates, or intermediate drawdowns in broader financial planning.

The line chart treats the start of investment as Year 0 and plots year-end values for both the compound and simple interest models on the same coordinates with distinct colors.

The vertical axis represents monetary amounts and the horizontal axis represents elapsed years. Hovering over a specific year on a desktop device displays that year's compound asset value, simple asset value, and difference in the information pane below.

This visualizes annual projections under constant rates rather than serving as a market price chart for stocks or mutual funds.

The final-year summary displays total compound assets, the simple model result, and their difference after the designated period.

In the annual comparison table below, one can review invested principal, compound model, simple model, and compound minus simple year by year from Year 1 to the final year.

Selecting a 40-year horizon generates 40 rows, requiring horizontal scrolling on narrow screens to inspect all columns.

Internal monthly calculations retain floating-point decimals for balances and interest, carrying them forward into subsequent months.

They do not truncate fractions of a yen mid-month or feed rounded year-end display values back into the next month's calculation.

Year-end compound and simple model figures placed in charts and tables are rounded to the nearest yen using Math.round, and differences are computed by subtracting those two displayed values.

This rounding approach reflects the display design of this tool. It does not replicate interest settlement dates, unit holdings, taxation, or fraction rounding specific to individual financial products.

For this reason, entering identical yields and durations will not guarantee exact yen-for-yen matching with real-world product statements.

This tool assumes that the specified constant annual yield remains unchanged throughout the entire 1 to 40-year duration. In actual stock and mutual fund investments, market prices fluctuate upward and downward, and returns may fall below principal.

Because volatility, the sequence of down and up periods, and changing unit counts due to varying purchase prices are replaced by a single static rate, this is not a simulation forecasting future market performance or investment outcomes.

Factors excluded from calculations include taxes, purchase and redemption fees, ongoing maintenance costs such as trust fees, dividend distributions and their reinvestment conditions, foreign exchange fluctuations, and changes in purchasing power due to inflation.

Japanese tax-exempt NISA frameworks, annual or lifetime contribution limits, and account designations are also not modeled. Changing monthly contributions mid-way, pausing investments, adding ad-hoc lump sums, or making partial withdrawals are not supported.

The tool does not reverse-calculate required savings amounts or durations from a target sum, assess risk tolerance, generate market-data-driven forecasts, recommend portfolios, or export CSV or PDF reports.

Its scope is strictly forward calculation of principal and two static-rate models from the four parameters entered on screen.

Displayed figures represent neither guaranteed future returns nor capital protection. The tool does not solicit or recommend specific financial products or provide personalized investment advice; use it as an analytical aid to understand the mathematical mechanics of compound versus simple interest.

Actual costs, tax treatment, product terms, and risks must be confirmed in the latest disclosures provided by respective financial institutions.