How this calculator works
The opening fund earns the assumed return while regular withdrawals reduce it. The final balance goal acts as a reserve. The nominal return is converted to the selected payment interval before valuing cash flows. The first cash flow is the entered amount; later cash flows grow by the equivalent periodic growth rate. Choose beginning or end timing and yearly summaries or individual payment rows. Enter a whole number of payment periods. Time solving finds the first payment period reaching the goal, adjusting the last cash flow to finish there; this mode supports non-negative returns and cash flow growth up to a 100-year horizon. Rate solving searches nominal annual returns from -99% to 200%. Dates use a 365.25-day model year and are illustrative rather than bank settlement dates. This is a finite fund calculation. An insurer lifetime annuity also depends on mortality, guarantees and expenses; these outputs are not an insurer quote.
Formula
Let j be the nominal annual return, m the compounding count and q payments per year. i = (1 + j/m)^(m/q) - 1, or exp(j/q) - 1 for continuous compounding. g = (1 + annual cash flow growth)^(1/q) - 1. For n payments, A = ((1+i)^n - (1+g)^n)/(i-g), with A = n(1+i)^(n-1) when i=g. Multiply A by (1+i) for beginning payments. Closing balance = opening balance x (1+i)^n + signed first payment x A. For withdrawals the signed cash flow is negative.
Worked example
$1,000 with zero return supports ten year-end withdrawals of $100 and leaves no reserve. A $210 fund earning 10% annually pays $121 at each of two year ends: $210 x 1.1 - $121 = $110, then $110 x 1.1 - $121 = $0.
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Frequently asked questions
Is this a guaranteed lifetime income quote?
No. It models a fixed fund and assumed returns over a stated horizon. Lifetime insurance payments also use mortality and contract terms.
What if withdrawals never exhaust the fund?
A time-solving request is rejected if the reserve is not reached within 100 years. Choose a higher withdrawal or use final-balance mode to inspect a specific horizon.
Do withdrawals rise with inflation?
Only if you enter the corresponding annual cash flow growth. The inflation field itself adjusts purchasing power and does not change nominal withdrawals.