Working backward from a retirement target: formulas and scenarios

These 144 scenarios are original calculations for checking the article's examples. They do not forecast investment performance.

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Assumptions

The U.S. edition targets $1 million at age 65, with starting ages 20, 30, 40 and 50 and starting balances of $0, $100,000 and $250,000. The Japanese edition independently uses ¥20 million and starting balances of ¥0, ¥5 million and ¥10 million. These are separate examples, not currency conversions. Hypothetical effective annual returns are 0%, 4% and 7%.

Targets are either fixed nominal amounts or amounts preserving today's purchasing power. Only the latter increases the future target by an assumed 2% annual inflation rate. Contributions remain fixed in nominal currency, rather than rising with inflation. Deposits occur at month-end and returns follow a smooth constant rate. Taxes, fees, market paths and interrupted contributions are excluded.

Formulas

Let a be the effective annual return, i annual inflation, n the remaining number of months, P the starting balance and T0 the target. Express rates as decimals: 4% is 0.04.

The equivalent monthly rate is r = (1 + a)^(1/12) − 1. The starting-balance growth factor is g = (1 + a)^(n/12). The nominal target is T = T0; the purchasing-power target is T = T0 × (1 + i)^(n/12). The month-end annuity factor is A = ((1 + r)^n − 1) / r, or A = n when r is zero.

The required monthly contribution is C = max(0, (T − P × g) / A). If the modeled starting balance alone meets the target, C is zero. The annual rate is not simply divided by 12. The CSV records unrounded calculated values; displayed article amounts are rounded for readability.

Reading the CSV

locale and currency distinguish en-US / USD and ja-JP / JPY. start_age, target_age, initial, annual_effective_return and assumed_annual_inflation describe the assumptions. target_mode and target_at_retirement describe the target basis and future amount; monthly_contribution is the required monthly amount and modeled_final_balance the modeled ending balance. No outcome is guaranteed. A personal plan also needs pension benefits, spending, taxes and fees.