Lump sum: $5,000.00
Annual contribution: $3,000.00
Years until college: 12
Annual return: 7.00%
Capital-gains tax rate: 15.00%
Future value: $64,926.31
Total contributions: $41,000.00
Tax-free growth: $23,926.31
Tax saved vs taxable account: $3,588.95
Taxable-account value: $61,337.36
Branch: Years 18: Lump $5,000.00, annual $3,000.00, years 18, return 7.00%, tax 15.00%, future value $118,896.76, contributions $59,000.00, growth $59,896.76, tax saved $8,984.51, taxable $109,912.25
Branch: Annual $5,000: Lump $5,000.00, annual $5,000.00, years 12, return 7.00%, tax 15.00%, future value $100,703.21, contributions $65,000.00, growth $35,703.21, tax saved $5,355.48, taxable $95,347.73
Branch: Return 5%: Lump $5,000.00, annual $3,000.00, years 12, return 5.00%, tax 15.00%, future value $56,730.66, contributions $41,000.00, growth $15,730.66, tax saved $2,359.60, taxable $54,371.06
Branch: Lump $0: Lump $0.00, annual $3,000.00, years 12, return 7.00%, tax 15.00%, future value $53,665.35, contributions $36,000.00, growth $17,665.35, tax saved $2,649.80, taxable $51,015.55
Branch: Tax rate 22%: Lump $5,000.00, annual $3,000.00, years 12, return 7.00%, tax 22.00%, future value $64,926.31, contributions $41,000.00, growth $23,926.31, tax saved $5,263.79, taxable $59,662.52
Branch: Years 4: Lump $5,000.00, annual $3,000.00, years 4, return 7.00%, tax 15.00%, future value $19,873.81, contributions $17,000.00, growth $2,873.81, tax saved $431.07, taxable $19,442.74
Branch: Lump $10,000, annual $5,000, 18 years: Lump $10,000.00, annual $5,000.00, years 18, return 7.00%, tax 15.00%, future value $203,794.49, contributions $100,000.00, growth $103,794.49, tax saved $15,569.17, taxable $188,225.31
Reverse: annual contribution for a future value of exactly $100,000: $4,960.69 ($4,960.69) — the star is DOLLARS
Exact annual contribution for a future value of exactly $100,000: $4960.6889
At $4,960.69 the figures are: Lump $5,000.00, annual $4,960.69, years 12, return 7.00%, tax 15.00%, future value $100,000.02, contributions $64,528.28, growth $35,471.74, tax saved $5,320.76, taxable $94,679.26
$0.01 less, $4,960.68, the figures are: Lump $5,000.00, annual $4,960.68, years 12, return 7.00%, tax 15.00%, future value $99,999.84, contributions $64,528.16, growth $35,471.68, tax saved $5,320.75, taxable $94,679.09
$0.01 more than the R1 star: —
Reverse verdict: CONTINUOUS
Reverse: years for a future value of at least $50,000: 10 years (10 years) — the star is YEARS
Exact years for a future value of at least $50,000: 10
At 10 years the figures are: Lump $5,000.00, annual $3,000.00, years 10, return 7.00%, tax 15.00%, future value $51,285.10, contributions $35,000.00, growth $16,285.10, tax saved $2,442.77, taxable $48,842.33
At 9 years the figures are: Lump $5,000.00, annual $3,000.00, years 9, return 7.00%, tax 15.00%, future value $45,126.26, contributions $32,000.00, growth $13,126.26, tax saved $1,968.94, taxable $43,157.32
One year more than the R2 star: —
Reverse verdict: STEP
Reverse: annual return for a future value of exactly $75,000: 9.10% (9.10%) — the star is a PERCENT
Exact annual return for a future value of exactly $75,000: 9.0994%
At 9.10% the figures are: Lump $5,000.00, annual $3,000.00, years 12, return 9.10%, tax 15.00%, future value $75,003.11, contributions $41,000.00, growth $34,003.11, tax saved $5,100.47, taxable $69,902.64
At 9.09% the figures are: Lump $5,000.00, annual $3,000.00, years 12, return 9.09%, tax 15.00%, future value $74,951.17, contributions $41,000.00, growth $33,951.17, tax saved $5,092.67, taxable $69,858.49
At 9.11% the figures are: Lump $5,000.00, annual $3,000.00, years 12, return 9.11%, tax 15.00%, future value $75,055.09, contributions $41,000.00, growth $34,055.09, tax saved $5,108.26, taxable $69,946.83
Reverse verdict: CONTINUOUS
Reverse: lump sum for a future value of exactly $60,000: $2,812.66 ($2,812.66) — the star is DOLLARS
Exact lump sum for a future value of exactly $60,000: $2812.6587
At $2,812.66 the figures are: Lump $2,812.66, annual $3,000.00, years 12, return 7.00%, tax 15.00%, future value $60,000.00, contributions $38,812.66, growth $21,187.34, tax saved $3,178.10, taxable $56,821.90
$1 less, $2,811.66, the figures are: Lump $2,811.66, annual $3,000.00, years 12, return 7.00%, tax 15.00%, future value $59,997.75, contributions $38,811.66, growth $21,186.09, tax saved $3,177.91, taxable $56,819.84
$1 more than the R4 star: —
Reverse verdict: CONTINUOUS
Reverse: capital-gains tax rate for a tax saved of exactly $5,000: 20.90% (20.90%) — the star is a PERCENT
Exact capital-gains tax rate for a tax saved of exactly $5,000: 20.8975%
At 20.90% the figures are: Lump $5,000.00, annual $3,000.00, years 12, return 7.00%, tax 20.90%, future value $64,926.31, contributions $41,000.00, growth $23,926.31, tax saved $5,000.60, taxable $59,925.71
At 20.89% the figures are: Lump $5,000.00, annual $3,000.00, years 12, return 7.00%, tax 20.89%, future value $64,926.31, contributions $41,000.00, growth $23,926.31, tax saved $4,998.21, taxable $59,928.10
At 20.91% the figures are: Lump $5,000.00, annual $3,000.00, years 12, return 7.00%, tax 20.91%, future value $64,926.31, contributions $41,000.00, growth $23,926.31, tax saved $5,002.99, taxable $59,923.32
Reverse verdict: CONTINUOUS
Reverse: years for a tax saved of at least $5,000: 14 years (14 years) — the star is YEARS
Exact years for a tax saved of at least $5,000: 14
At 14 years the figures are: Lump $5,000.00, annual $3,000.00, years 14, return 7.00%, tax 15.00%, future value $80,544.13, contributions $47,000.00, growth $33,544.13, tax saved $5,031.62, taxable $75,512.51
At 13 years the figures are: Lump $5,000.00, annual $3,000.00, years 13, return 7.00%, tax 15.00%, future value $72,471.15, contributions $44,000.00, growth $28,471.15, tax saved $4,270.67, taxable $68,200.48
One year more than the R6 star: —
Reverse verdict: STEP
Edge: years 0: Lump $5,000.00, annual $3,000.00, years 0, return 7.00%, tax 15.00%, future value $5,000.00, contributions $5,000.00, growth $0.00, tax saved $0.00, taxable $5,000.00
Edge: contributions $0: Lump $0.00, annual $0.00, years 12, return 7.00%, tax 15.00%, future value $0.00, contributions $0.00, growth $0.00, tax saved $0.00, taxable $0.00
Edge: return 0%: Lump $5,000.00, annual $3,000.00, years 12, return 0.00%, tax 15.00%, future value $41,000.00, contributions $41,000.00, growth $0.00, tax saved $0.00, taxable $41,000.00
Edge: years 1: Lump $5,000.00, annual $3,000.00, years 1, return 7.00%, tax 15.00%, future value $8,350.00, contributions $8,000.00, growth $350.00, tax saved $52.50, taxable $8,297.50
Edge: lump $100,000: Lump $100,000.00, annual $3,000.00, years 12, return 7.00%, tax 15.00%, future value $278,884.51, contributions $136,000.00, growth $142,884.51, tax saved $21,432.68, taxable $257,451.84
Edge: tax rate 0%: Lump $5,000.00, annual $3,000.00, years 12, return 7.00%, tax 0.00%, future value $64,926.31, contributions $41,000.00, growth $23,926.31, tax saved $0.00, taxable $64,926.31
Years 18: Lump $5,000.00, annual $3,000.00, years 18, return 7.00%, tax 15.00%, future value $118,896.76, contributions $59,000.00, growth $59,896.76, tax saved $8,984.51, taxable $109,912.25.
Annual $5,000: Lump $5,000.00, annual $5,000.00, years 12, return 7.00%, tax 15.00%, future value $100,703.21, contributions $65,000.00, growth $35,703.21, tax saved $5,355.48, taxable $95,347.73.
Return 5%: Lump $5,000.00, annual $3,000.00, years 12, return 5.00%, tax 15.00%, future value $56,730.66, contributions $41,000.00, growth $15,730.66, tax saved $2,359.60, taxable $54,371.06.
Lump $0: Lump $0.00, annual $3,000.00, years 12, return 7.00%, tax 15.00%, future value $53,665.35, contributions $36,000.00, growth $17,665.35, tax saved $2,649.80, taxable $51,015.55.
Tax rate 22%: Lump $5,000.00, annual $3,000.00, years 12, return 7.00%, tax 22.00%, future value $64,926.31, contributions $41,000.00, growth $23,926.31, tax saved $5,263.79, taxable $59,662.52.
Years 4: Lump $5,000.00, annual $3,000.00, years 4, return 7.00%, tax 15.00%, future value $19,873.81, contributions $17,000.00, growth $2,873.81, tax saved $431.07, taxable $19,442.74.
Lump $10,000, annual $5,000, 18 years: Lump $10,000.00, annual $5,000.00, years 18, return 7.00%, tax 15.00%, future value $203,794.49, contributions $100,000.00, growth $103,794.49, tax saved $15,569.17, taxable $188,225.31.
Reverse: the annual contribution for a future value of exactly $100,000 is $4,960.69 (exact $4960.6889); at $4,960.69 the future value is $100,000.02; $0.01 less, $4,960.68, it is $99,999.84 — verdict: CONTINUOUS. The years for a future value of at least $50,000 are 10 years; at 10 years the future value is $51,285.10; 9 years gives $45,126.26 — verdict: STEP. The annual return for a future value of exactly $75,000 is 9.10% (exact 9.0994%); at 9.10% the future value is $75,003.11; 9.09% gives $74,951.17; 9.11% gives $75,055.09 — verdict: CONTINUOUS. The lump sum for a future value of exactly $60,000 is $2,812.66 (exact $2812.6587); at $2,812.66 the future value is $60,000.00; $1 less, $2,811.66, it is $59,997.75 — verdict: CONTINUOUS. The capital-gains tax rate for a tax saved of exactly $5,000 is 20.90% (exact 20.8975%); at 20.90% the tax saved is $5,000.60; 20.89% gives $4,998.21; 20.91% gives $5,002.99 — verdict: CONTINUOUS. The years for a tax saved of at least $5,000 are 14 years; at 14 years the tax saved is $5,031.62; 13 years gives $4,270.67 — verdict: STEP.
Edges: years 0 gives Lump $5,000.00, annual $3,000.00, years 0, return 7.00%, tax 15.00%, future value $5,000.00, contributions $5,000.00, growth $0.00, tax saved $0.00, taxable $5,000.00. Contributions $0 gives Lump $0.00, annual $0.00, years 12, return 7.00%, tax 15.00%, future value $0.00, contributions $0.00, growth $0.00, tax saved $0.00, taxable $0.00. Return 0% gives Lump $5,000.00, annual $3,000.00, years 12, return 0.00%, tax 15.00%, future value $41,000.00, contributions $41,000.00, growth $0.00, tax saved $0.00, taxable $41,000.00. Years 1 gives Lump $5,000.00, annual $3,000.00, years 1, return 7.00%, tax 15.00%, future value $8,350.00, contributions $8,000.00, growth $350.00, tax saved $52.50, taxable $8,297.50. Lump $100,000 gives Lump $100,000.00, annual $3,000.00, years 12, return 7.00%, tax 15.00%, future value $278,884.51, contributions $136,000.00, growth $142,884.51, tax saved $21,432.68, taxable $257,451.84. Tax rate 0% gives Lump $5,000.00, annual $3,000.00, years 12, return 7.00%, tax 0.00%, future value $64,926.31, contributions $41,000.00, growth $23,926.31, tax saved $0.00, taxable $64,926.31.