Retirement balance: $1,000,000.00
First-year withdrawal rate: 4.00%
Expected annual return: 6.00%
Annual inflation: 3.00%
Years in retirement: 30 years
First-year withdrawal: $40,000.00
Monthly income: $3,333.33/mo
Year-5 withdrawal: $45,020.35
Year-10 withdrawal: $52,190.93
Year-20 withdrawal: $70,140.24
Year-30 withdrawal: $94,262.62
Ending balance after 30 years: $1,321,852.90
Total withdrawn over 30 years: $1,903,016.63
Runs out in: year 49
Shortfall that year: $117,542.10
Branch: Balance $500,000: First-year $20,000.00 ($1,666.67/mo), year-30 withdrawal $47,131.31, ending balance $660,926.45, total withdrawn $951,508.31, runs out in year 49 (shortfall $58,771.05)
Branch: Balance $2,000,000: First-year $80,000.00 ($6,666.67/mo), year-30 withdrawal $188,525.24, ending balance $2,643,705.81, total withdrawn $3,806,033.26, runs out in year 49 (shortfall $235,084.19)
Branch: Withdrawal rate 3%: First-year $30,000.00 ($2,500.00/mo), year-30 withdrawal $70,696.97, ending balance $2,427,262.47, total withdrawn $1,427,262.47, never runs out (100+ years)
Branch: Withdrawal rate 5%: First-year $50,000.00 ($4,166.67/mo), year-30 withdrawal $117,828.28, ending balance $216,443.34, total withdrawn $2,378,770.79, runs out in year 32 (shortfall $10,453.20)
Branch: Return 4%: First-year $40,000.00 ($3,333.33/mo), year-30 withdrawal $94,262.62, RUNS OUT in year 30 (shortfall $21,142.65), total withdrawn $1,881,873.98, no money left after year 30
Branch: Return 8%: First-year $40,000.00 ($3,333.33/mo), year-30 withdrawal $94,262.62, ending balance $3,954,341.35, total withdrawn $1,903,016.63, never runs out (100+ years)
Branch: Inflation 0%: First-year $40,000.00 ($3,333.33/mo), year-30 withdrawal $40,000.00, ending balance $2,581,163.72, total withdrawn $1,200,000.00, never runs out (100+ years)
Branch: Inflation 5%: First-year $40,000.00 ($3,333.33/mo), year-30 withdrawal $164,645.42, ending balance $57,295.98, total withdrawn $2,657,553.90, runs out in year 31 (shortfall $112,143.95)
Branch: Years 20: First-year $40,000.00 ($3,333.33/mo), year-20 withdrawal $70,140.24, ending balance $1,339,103.16, total withdrawn $1,074,814.98, runs out in year 49 (shortfall $117,542.10)
Branch: Years 40: First-year $40,000.00 ($3,333.33/mo), year-40 withdrawal $126,681.08, ending balance $920,811.08, total withdrawn $3,016,050.39, runs out in year 49 (shortfall $117,542.10)
Reverse: withdrawal rate for the money to run out exactly at year 30: 5.20% (5.20%) — the star is a PERCENT
Exact withdrawal rate for the money to run out exactly at year 30: 5.1958%
At 5.20% the figures are: First-year $52,000.00 ($4,333.33/mo), year-30 withdrawal $122,541.41, RUNS OUT in year 30 (shortfall $4,638.58), total withdrawn $2,469,283.04, no money left after year 30
At 5.19% the figures are: First-year $51,900.00 ($4,325.00/mo), year-30 withdrawal $122,305.75, ending balance $6,415.52, total withdrawn $2,469,164.08, runs out in year 31 (shortfall $119,174.47)
Reverse verdict: SMALLEST-STEP
Reverse: balance for a $60,000 first-year withdrawal to last 30 years: $1,154,778.03 ($1,154,778.03) — the star is DOLLARS
Exact balance for a $60,000 first-year withdrawal to last 30 years: $1154778.0268
At $1,154,778.03 the figures are: First-year $60,000.00 ($5,000.00/mo), year-30 withdrawal $141,393.93, ending balance $0.02, total withdrawn $2,854,524.94, runs out in year 31 (shortfall $145,635.73)
One dollar less, $1,154,777.03, the figures are: First-year $60,000.00 ($5,000.00/mo), year-30 withdrawal $141,393.93, RUNS OUT in year 30 (shortfall $5.72), total withdrawn $2,854,519.22, no money left after year 30
One cent less, $1,154,778.02, the ending balance is: -$0.04
Reverse verdict: CONTINUOUS
Reverse: return for a 5% withdrawal rate to last 30 years: 5.70% (5.70%) — the star is a PERCENT
Exact return for a 5% withdrawal rate to last 30 years: 5.6983%
At 5.70% the figures are: First-year $50,000.00 ($4,166.67/mo), year-30 withdrawal $117,828.28, ending balance $1,131.01, total withdrawn $2,378,770.79, runs out in year 31 (shortfall $120,167.65)
At 5.69% the figures are: First-year $50,000.00 ($4,166.67/mo), year-30 withdrawal $117,828.28, RUNS OUT in year 30 (shortfall $5,635.83), total withdrawn $2,373,134.96, no money left after year 30
Reverse verdict: SMALLEST-STEP
Reverse: inflation rate at which the money runs out exactly at year 30: 5.08% (5.08%) — the star is a PERCENT
Exact inflation rate at which the money runs out exactly at year 30: 5.0762%
At 5.08% the figures are: First-year $40,000.00 ($3,333.33/mo), year-30 withdrawal $168,322.38, RUNS OUT in year 30 (shortfall $2,867.00), total withdrawn $2,691,486.39, no money left after year 30
At 5.07% the figures are: First-year $40,000.00 ($3,333.33/mo), year-30 withdrawal $167,858.46, ending balance $4,699.12, total withdrawn $2,689,721.52, runs out in year 31 (shortfall $171,387.81)
Reverse verdict: SMALLEST-STEP
Reverse: first year the withdrawal passes $50,000: Year 9 (Year 9) — the star is a YEAR
Exact year the withdrawal passes $50,000: —
In year 9 the withdrawal is: Year 9 — $50,670.80
In year 8 the withdrawal is: Year 8 — $49,194.95
Reverse verdict: DISCRETE-SCAN
Reverse: balance for a fixed $40,000 a year to last 40 years: $910,476.73 ($910,476.73) — the star is DOLLARS
Exact balance for a fixed $40,000 a year to last 40 years: $910476.7326
At $910,476.73 the figures are: First-year $40,000.00 ($3,333.33/mo), year-40 withdrawal $126,681.08, RUNS OUT in year 40 (shortfall $0.03), total withdrawn $3,016,050.36, no money left after year 40
One dollar less, $910,475.73, the figures are: First-year $40,000.00 ($3,333.33/mo), year-40 withdrawal $126,681.08, RUNS OUT in year 40 (shortfall $10.31), total withdrawn $3,016,040.08, no money left after year 40
One cent less, $910,476.72, the ending balance is: -$0.13
Reverse verdict: CONTINUOUS
Edge: withdrawal rate 0%: First-year $0.00 ($0.00/mo), year-30 withdrawal $0.00, ending balance $5,743,491.17, total withdrawn $0.00, never runs out (100+ years)
Edge: return 0% and inflation 0%: First-year $40,000.00 ($3,333.33/mo), year-30 withdrawal $40,000.00, RUNS OUT in year 26 (shortfall $40,000.00), total withdrawn $1,000,000.00, no money left after year 26
Edge: balance $0: First-year $0.00 ($0.00/mo), year-30 withdrawal $0.00, ending balance $0.00, total withdrawn $0.00, never runs out (100+ years)
Edge: years 1: First-year $40,000.00 ($3,333.33/mo), year-1 withdrawal $40,000.00, ending balance $1,020,000.00, total withdrawn $40,000.00, runs out in year 49 (shortfall $117,542.10)
Edge: return 10%: First-year $40,000.00 ($3,333.33/mo), year-30 withdrawal $94,262.62, ending balance $8,865,322.38, total withdrawn $1,903,016.63, never runs out (100+ years)
Edge: inflation 6%: First-year $40,000.00 ($3,333.33/mo), year-30 withdrawal $216,735.52, RUNS OUT in year 27 (shortfall $90,987.66), total withdrawn $2,457,242.97, no money left after year 27
Balance $500,000: First-year $20,000.00 ($1,666.67/mo), year-30 withdrawal $47,131.31, ending balance $660,926.45, total withdrawn $951,508.31, runs out in year 49 (shortfall $58,771.05).
Balance $2,000,000: First-year $80,000.00 ($6,666.67/mo), year-30 withdrawal $188,525.24, ending balance $2,643,705.81, total withdrawn $3,806,033.26, runs out in year 49 (shortfall $235,084.19).
Withdrawal rate 3%: First-year $30,000.00 ($2,500.00/mo), year-30 withdrawal $70,696.97, ending balance $2,427,262.47, total withdrawn $1,427,262.47, never runs out (100+ years).
Withdrawal rate 5%: First-year $50,000.00 ($4,166.67/mo), year-30 withdrawal $117,828.28, ending balance $216,443.34, total withdrawn $2,378,770.79, runs out in year 32 (shortfall $10,453.20).
Return 4%: First-year $40,000.00 ($3,333.33/mo), year-30 withdrawal $94,262.62, RUNS OUT in year 30 (shortfall $21,142.65), total withdrawn $1,881,873.98, no money left after year 30.
Return 8%: First-year $40,000.00 ($3,333.33/mo), year-30 withdrawal $94,262.62, ending balance $3,954,341.35, total withdrawn $1,903,016.63, never runs out (100+ years).
Inflation 0%: First-year $40,000.00 ($3,333.33/mo), year-30 withdrawal $40,000.00, ending balance $2,581,163.72, total withdrawn $1,200,000.00, never runs out (100+ years).
Inflation 5%: First-year $40,000.00 ($3,333.33/mo), year-30 withdrawal $164,645.42, ending balance $57,295.98, total withdrawn $2,657,553.90, runs out in year 31 (shortfall $112,143.95).
Years 20: First-year $40,000.00 ($3,333.33/mo), year-20 withdrawal $70,140.24, ending balance $1,339,103.16, total withdrawn $1,074,814.98, runs out in year 49 (shortfall $117,542.10).
Years 40: First-year $40,000.00 ($3,333.33/mo), year-40 withdrawal $126,681.08, ending balance $920,811.08, total withdrawn $3,016,050.39, runs out in year 49 (shortfall $117,542.10).
Reverse: the withdrawal rate for the money to run out exactly at year 30 is 5.20% (exact 5.1958%); at 5.20% the ending balance is -$4,638.58 (runs out in year 30); at 5.19% it is $6,415.52 (lasts the 30-year plan) — verdict: SMALLEST-STEP. The balance for a $60,000 first-year withdrawal to last 30 years is $1,154,778.03 (exact $1154778.0268); at $1,154,778.03 the ending balance is $0.02; $1 less, $1,154,777.03, it is -$5.72; one cent less, $1,154,778.02, it is -$0.04 — one cent less does NOT round to the same figure (leverage x5.74) — verdict: CONTINUOUS. The return needed for a 5% withdrawal rate to last 30 years is 5.70% (exact 5.6983%); at 5.70% the ending balance is $1,131.01; at 5.69% it is -$5,635.83 — verdict: SMALLEST-STEP. The inflation rate at which the money runs out exactly at year 30 is 5.08% (exact 5.0762%); at 5.08% the ending balance is -$2,867.00 (runs out in year 30); at 5.07% it is $4,699.12 (lasts) — verdict: SMALLEST-STEP. The first year the withdrawal passes $50,000 is year 9 ($50,670.80); year 8 is $49,194.95 — verdict: DISCRETE-SCAN. The balance for a fixed $40,000 a year to last 40 years is $910,476.73 (exact $910476.7326); at $910,476.73 the ending balance is -$0.03 (slightly negative — the star is the rounded exact); $1 less, $910,475.73, it is -$10.31; one cent less, $910,476.72, it is -$0.13 — one cent less does NOT round to the same figure (leverage x10.29) — verdict: CONTINUOUS.