Definitions

Clear definitions in «X — is Y» format.

Compound interest: Compound interest is earning return not only on the initial amount but also on previously accumulated interest. The base grows each period, multiplying the effect.
Real return: Real return is return minus inflation. Formula: r_real = (1+r)/(1+inf) − 1. Reflects how much purchasing power actually grows.
Real value: Real value is nominal amount converted to «today's money» with inflation. Formula: real = nom / (1+inf)^(m/12).
Safe withdrawal: Safe withdrawal is the maximum monthly spending at which real capital value doesn't decrease. Based on real return, not fixed 4%.

Formulas (LaTeX)

Calculation formulas used in the calculator. Variables: r — annual return (decimal), inf — annual inflation (decimal), m — months from start.

Converting annual return to monthly:

m_r = (1 + r)^{1/12} - 1

r — годовая доходность (доля, 15% → 0.15)

Recurrent balance calculation each month:

bal_m = bal_{m-1} \cdot (1 + m_r) + contrib_m

Converting nominal balance to today's money:

real = nom / (1 + inf)^{m/12}

nom — номинальный баланс, inf — годовая инфляция (доля), m — месяцы

Return minus inflation:

r_{real} = \frac{1+r}{1+inf} - 1

Maximum monthly spending without losing purchasing power:

safe = nom \cdot r_{real} / 12

Safe withdrawal is based on real return (nominal minus inflation). With negative real return, capital loses purchasing power.