Calculation Method and Verification
Each rule the calculator uses is shown with its formula and one example. The last section compares our results with values derived from the published formulas under the same assumptions.
Interest and Compounding Period
Interest this month = compounded principal × annual rate ÷ 12
Interest accrues each month with this formula, and at the end of each compounding period (monthly, semiannual or annual) the interest after taxes and fees is added to the principal.
Interest that has been added earns interest from the next period.
Example: With a compounded principal of $10,000 at 3% a year, this month's interest is $25. With semiannual compounding, six months' interest of $150 is added at the end of month 6.
Beginning or End of Month
Beginning: interest base = compounded principal + this month's deposit
End: interest base = compounded principal
With beginning-of-month deposits, the deposit earns interest from the same month; with end-of-month deposits, from the next month.
Example: With $500 a month at 12% a year, interest in month 1 is $5 at the beginning and $0 at the end.
Rounding
Interest this month = rounded (interest accrued in the period) − interest already recorded in earlier months
The interest accrued in the period is rounded down, to the nearest, or up to the cent (yen for Japanese yen), and the difference from the earlier total becomes this month's interest.
Monthly rounding does not pile up within a period.
Example: If accrued interest is $25.006, it becomes $25.00 when rounded down and $25.01 when rounded to the nearest cent.
Three Tax Methods
Tax per compounding: tax = (interest in the period − fees in the period) × tax rate
Tax on sale: tax = (value in the last month − total principal) × tax rate
Tax-free deducts no tax.
Tax per compounding deducts tax each compounding period before adding interest to the principal.
Tax on sale deducts no tax while invested and deducts it all in the last month. When withdrawing, tax is deducted at each withdrawal in proportion to the gain at that point.
Tax amounts are rounded down to the cent (yen).
Example: With $100 of interest in the period and a 20.315% tax rate, tax per compounding is $20.31.
Fees
Fee this month = month-end value × annual fee rate ÷ 12
Fees such as expense ratios apply to the month-end value including that month's deposit and interest, rounded the same way as interest.
Because fees also apply to that month's deposit, the result is not the same as lowering the return by the same amount.
Example: With a month-end value of $30,000 and a 0.6% annual fee, this month's fee is $15.
Inflation
Real value = final amount ÷ (1 + inflation rate) ^ years
If you enter an expected inflation rate, the final amount in today's prices is shown next to it.
Example: A final amount of $200,000 with 2% inflation over 20 years has a real value of about $134,594.
Annual Increase and Extra Deposits
Percent: this year's monthly deposit = last year's amount × (1 + increase rate)
Amount: this year's monthly deposit = last year's amount + increase amount
The increase applies when a new year starts (months 13, 25, …), rounded to the nearest cent (yen).
Extra deposits are added in the two months you choose each year, counting your first month of saving as month 1. They follow the same beginning or end-of-month rule as that month's deposit and are not increased.
Example: With $500 a month and a 10% annual increase, the deposit is $550 in year 2 and $605 in year 3.
Comparison with the Published Formulas
This table compares our results with values from the published compound interest formulas for the same conditions (rounded down, tax-free).
| This site | Published formula | Difference |
|---|---|---|
| ¥50,000 a month, 5% a year, 20 years | ||
| ¥20,551,482 | ¥20,551,683 | −¥201 |
| ¥30,000 a month, 3% a year, 30 years | ||
| ¥17,481,827 | ¥17,482,107 | −¥280 |
| This site | Published formula | Difference |
|---|---|---|
| $10,000 up front, 7% a year, 10 years, compounded annually | ||
| $19,671.47 | $19,671.51 | −$0.04 |
| $10,000 up front, 5% a year, 10 years, compounded monthly | ||
| $16,469.32 | $16,470.09 | −$0.77 |
The difference is the interest below one yen (one cent in the dollar table) rounded down each month.
Published formula values are derived from the compound interest formulas published by Japan's Financial Services Agency and the U.S. Securities and Exchange Commission under the same assumptions; they are not the output of either agency's calculator. Formulas: deposits = monthly deposit × ((1 + monthly rate) ^ months − 1) ÷ monthly rate; lump sum = principal × (1 + period rate) ^ periods. Checked with the formulas on: October 11, 2026
This tool is for informational purposes only and does not constitute investment advice or a solicitation to buy or sell any financial product. Simulation results do not guarantee future outcomes. Investment decisions are your own responsibility.