About Compound Interest
Basic Concept
Compound interest is a method where earned interest is added back to the principal, and subsequent interest is calculated on the new, larger total. In contrast, simple interest always calculates interest based only on the original principal.
For example, if you invest $10,000 at 5% annual interest, simple interest yields $500 every year. With compound interest, from the second year onward, interest is also earned on the previous year's interest, so the gap between simple and compound interest widens over time. This is known as the “compound interest effect” and plays a crucial role in long-term wealth building.
Input Parameters
Compounding Method (Monthly / Semi-annual / Annual)
The compounding method determines how frequently interest is added to the principal. Under every method, interest accrues each month as simple interest (principal × annual rate ÷ 12); monthly compounding adds it to the principal every month, semi-annual every 6 months, and annual every 12 months. Because added interest starts earning interest from the next period, a higher frequency leads to a greater compound interest effect, so monthly compounding yields the highest final balance at the same annual rate. Money deposited partway through a period earns interest only for the months elapsed until it is added.
Interest Timing (Beginning / End of Period)
Beginning-of-period adds your deposit to the principal before calculating interest, so your deposit earns interest immediately. End-of-period calculates interest first, then adds the deposit. Under the same conditions, beginning-of-period results in a higher final balance.
Tax Mode (Tax-free / Taxed per Period / Taxed on Sale)
Tax-free mode calculates interest without deducting any tax, applicable to tax-advantaged accounts such as NISA in Japan. Taxed-per-period mode deducts tax at a specified rate each time interest is calculated. This corresponds to the withholding tax on bank deposit interest in Japan (20.315%). Taxed on sale applies no tax while invested; at the end, the tax rate is applied to the difference between the final balance and the total of the initial principal and deposits (no tax if that difference is a loss).
Formulas
The main formulas used in this calculator are shown below. P_m is the balance on which interest accrues in month m (principal plus interest already added; under beginning-of-period timing it includes that month's deposit), r is the annual interest rate (as a decimal), t is the tax rate (%), A is the after-tax total, and D is the total amount deposited. Interest accrues every month and the accumulated amount is added to the principal at the interval set by the compounding method (monthly compounding adds each month's interest immediately).
* Tax rounding uses floor (truncation), following Japanese tax conventions. Interest rounding can be set to floor, round, or ceil depending on your preference.