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No injection (A)
With injection (B)
Target age
Projected value at exit age
A · No injection
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B · With injection
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Total invested (principal) by exit
A · No injection
—
B · With injection
—
Expected expense at exit age (inflated)
Monthly
—
Annual
—
Capital runs out at age
A · No injection
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B · With injection
—
Accumulation — value to exit age
How the portfolio grows while you invest.
No injection
With injection
Drawdown — balance after exit age
Balance after each year's inflated withdrawal.
No injection
With injection
05 Injection needed for a target exit value
Required annual injection to reach your target exit value
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Uses target exit, current value, growth & years from the inputs
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PMT = (Target − PV·(1+r)ⁿ) · r / ((1+r)ⁿ − 1). Ordinary annuity — injection at each year-end.
08 Injection needed to last until your target age
Years needed in retirement
—
Capital required at exit age
—
Required annual injection during accumulation to reach that capital
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Required capital = E₁ · (1 − ((1+g)/(1+r))ⁿ) / (1 − (1+g)/(1+r)) — growing-annuity PV, where E₁ = first-year retirement expense, g = inflation, r = post-exit growth, n = years in retirement.
§4 · Year-by-year accumulation▸
| Year | Age | A: value (no inj.) | A: invested | B: value (with inj.) | B: invested |
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§6 · Retirement drawdown▸
| Yr | Age | Expense (inflated) | A: balance (no inj.) | B: balance (with inj.) |
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