Annuity vs Lump Sum Calculator: Which Pays More 2026

How the comparison works

On the defaults — a $100,000.00 lump sum, an annuity paying $8,000.00 a year for 20 years, and a 5.00% discount rate — the annuity is worth $99,697.68 today, the lump sum would grow to $265,329.77 over the 20 years, and the annuity pays $160,000.00 in total — so the lump sum is worth $302.32 more in today’s money: LUMP SUM wins by $302.32.

The discount rate is the whole comparison. It is the return you could earn by investing the lump sum, so a higher rate makes the lump sum more attractive and a lower rate makes the annuity more attractive. At a 3.00% rate the annuity is worth $119,019.80 and wins by $19,019.80; at a 7.00% rate it is worth only $84,752.11 and the lump sum wins by $15,247.89. The rate that makes the two exactly equal is 4.96% — below it the annuity wins, above it the lump sum wins.

The lump sum growing to $265,329.77 while the annuity pays only $160,000.00 in total looks like a rout for the lump sum, but the two numbers are not on the same footing: the $265,329.77 is 20 years of compounding, while the $160,000.00 adds up payments received over 20 years without discounting them. A dollar in year 20 is not worth a dollar today — the first $8,000.00 payment is worth $7,619.05 today, but the twentieth is worth only $3,015.12 — and once every payment is discounted the annuity totals $99,697.68, a shade under the lump sum.

The worked example, line by line

Setup: $100,000.00 lump sum, $8,000.00 a year, 20 years, 5.00% discount rate.

Line 1 — the discount factor. The present value of $1 a year for 20 years at 5.00% is (1 − 1.05^−20) ÷ 0.05 = 12.4622. Each year’s payment is worth less than the last: the first $8,000.00 payment is worth $8,000.00 ÷ 1.05 = $7,619.05 today, and the twentieth is worth $8,000.00 ÷ 1.05^20 = $3,015.12.

Line 2 — the present value of the annuity. PV = $8,000.00 × 12.4622 = $99,697.68. That is what the whole 20-year stream of payments is worth in today’s money.

Line 3 — the lump-sum future value. 1.05^20 = 2.6533, so $100,000.00 × 2.6533 = $265,329.77 — what the lump sum becomes if it is invested at 5.00% for 20 years.

Line 4 — the total payments and the gap. Total payments = $8,000.00 × 20 = $160,000.00. Difference = $99,697.68 − $100,000.00 = -$302.32 — LUMP SUM wins by $302.32. The default result in full: Present value $99,697.68, lump sum $100,000.00, difference -$302.32 — LUMP SUM wins by $302.32; lump-sum future value $265,329.77, total payments $160,000.00.

Line 5 — the rounding convention. Rounding convention: every gap on this page is the difference of the displayed values: each side is rounded to cents first, then subtracted. On these defaults the unrounded gap and the displayed gap agree at -$302.32, but on other inputs they can differ by a cent, and the page always shows the displayed figure.

Every branch, checked

Annuity $9,000 a year: Present value $112,159.89, lump sum $100,000.00, difference $12,159.89 — ANNUITY wins by $12,159.89; lump-sum future value $265,329.77, total payments $180,000.00. Another $1,000.00 a year adds $12,462.21 of present value — the $9,000.00 annuity is worth more than the lump sum by a wide margin.

Discount rate 7%: Present value $84,752.11, lump sum $100,000.00, difference -$15,247.89 — LUMP SUM wins by $15,247.89; lump-sum future value $386,968.45, total payments $160,000.00. At 7.00% the lump sum compounds to $386,968.45, and the annuity’s later payments are discounted so hard that its present value falls to $84,752.11.

Years 30: Present value $122,979.61, lump sum $100,000.00, difference $22,979.61 — ANNUITY wins by $22,979.61; lump-sum future value $432,194.24, total payments $240,000.00. Ten more years of payments add $23,281.93 of present value — the extra decade is worth more than the whole default gap, many times over.

Lump sum $80,000: Present value $99,697.68, lump sum $80,000.00, difference $19,697.68 — ANNUITY wins by $19,697.68; lump-sum future value $212,263.82, total payments $160,000.00. The annuity’s value does not change — only the lump sum shrinks — so a $20,000.00 smaller lump sum flips the winner by exactly $20,000.00.

Discount rate 3%: Present value $119,019.80, lump sum $100,000.00, difference $19,019.80 — ANNUITY wins by $19,019.80; lump-sum future value $180,611.12, total payments $160,000.00. At 3.00% the lump sum only grows to $180,611.12, and the annuity’s later payments keep most of their value — the annuity wins by nearly a fifth of the lump sum.

Annuity $7,000 a year: Present value $87,235.47, lump sum $100,000.00, difference -$12,764.53 — LUMP SUM wins by $12,764.53; lump-sum future value $265,329.77, total payments $140,000.00. A $1,000.00 smaller payment costs the annuity $12,462.21 of present value, and the lump sum’s lead widens to $12,764.53.

The reverses, worked backwards

Annuity payment for a TIE: exact $8024.2587; displayed $8,024.26 → present value $100,000.02, lump sum $100,000.00, difference $0.02 — ANNUITY wins by $0.02; lump-sum future value $265,329.77, total payments $160,485.20. The displayed $8,024.26 gives a present value two cents OVER the tie — the payment rounding, not a real gap. At $8,023.26: Present value $99,987.55, lump sum $100,000.00, difference -$12.45 — LUMP SUM wins by $12.45; lump-sum future value $265,329.77, total payments $160,465.20. The star is DOLLARS/YEAR. This reverse is CONTINUOUS.

Discount rate for a TIE: exact 4.9643%; displayed 4.96% → present value $100,036.69, lump sum $100,000.00, difference $36.69 — ANNUITY wins by $36.69; lump-sum future value $263,315.51, total payments $160,000.00. At 4.95%: Present value $100,121.71, lump sum $100,000.00, difference $121.71 — ANNUITY wins by $121.71; lump-sum future value $262,814.22, total payments $160,000.00. At 4.97%: Present value $99,951.77, lump sum $100,000.00, difference -$48.23 — LUMP SUM wins by $48.23; lump-sum future value $263,817.71, total payments $160,000.00. The star is a PERCENT. This reverse is CONTINUOUS.

Years for PV of at least $110,000: exact 24 years; displayed 24 years → present value $110,389.13, lump sum $100,000.00, difference $10,389.13 — ANNUITY wins by $10,389.13; lump-sum future value $322,509.99, total payments $192,000.00. At 23 years: Present value $107,908.59, lump sum $100,000.00, difference $7,908.59 — ANNUITY wins by $7,908.59; lump-sum future value $307,152.38, total payments $184,000.00. 24 years is the smallest term that reaches $110,000 of present value — 23 years only reaches $107,908.59. The star is YEARS. This reverse is a STEP.

Lump sum for a TIE: exact $99697.6827; displayed $99,697.68 → present value $99,697.68, lump sum $99,697.68, difference $0.00 — TIE; lump-sum future value $264,527.63, total payments $160,000.00. At $99,696.68: Present value $99,697.68, lump sum $99,696.68, difference $1.00 — ANNUITY wins by $1.00; lump-sum future value $264,524.97, total payments $160,000.00. The star is DOLLARS. This reverse is CONTINUOUS.

Discount rate for lump-sum future value exactly $300,000: exact 5.6467%; displayed 5.65% → present value $94,424.48, lump sum $100,000.00, difference -$5,575.52 — LUMP SUM wins by $5,575.52; lump-sum future value $300,185.72, total payments $160,000.00. At 5.64%: Present value $94,502.36, lump sum $100,000.00, difference -$5,497.64 — LUMP SUM wins by $5,497.64; lump-sum future value $299,617.97, total payments $160,000.00. At 5.66%: Present value $94,346.70, lump sum $100,000.00, difference -$5,653.30 — LUMP SUM wins by $5,653.30; lump-sum future value $300,754.50, total payments $160,000.00. The star is a PERCENT. This reverse is CONTINUOUS.

Lump sum growing to exactly the total annuity payments: exact $60302.3173; displayed $60,302.32 → present value $99,697.68, lump sum $60,302.32, difference $39,395.36 — ANNUITY wins by $39,395.36; lump-sum future value $160,000.01, total payments $160,000.00. At $60,301.32: Present value $99,697.68, lump sum $60,301.32, difference $39,396.36 — ANNUITY wins by $39,396.36; lump-sum future value $159,997.35, total payments $160,000.00. The star is DOLLARS. This reverse is CONTINUOUS.

What the defaults assume

The discount rate is the whole comparison — a higher rate favours the lump sum (you can invest it), a lower rate favours the annuity. The annuity’s payments are assumed at the END of each year. Taxes are NOT modelled (a lump sum and annuity payments are often taxed differently — a real decision needs a tax adviser). Inflation is NOT modelled (the annuity’s $8,000.00 buys less in year 20). The annuity assumes the payer never defaults — a lump sum has no counterparty risk. With a 0.00% discount rate (Present value $160,000.00, lump sum $100,000.00, difference $60,000.00 — ANNUITY wins by $60,000.00; lump-sum future value $100,000.00, total payments $160,000.00) the annuity is just the sum of its payments — a model-level outcome, not an error. With 1 year (Present value $7,619.05, lump sum $100,000.00, difference -$92,380.95 — LUMP SUM wins by $92,380.95; lump-sum future value $105,000.00, total payments $8,000.00) a single $8,000.00 payment is worth only $7,619.05 today. With a $0.00 annuity (Present value $0.00, lump sum $100,000.00, difference -$100,000.00 — LUMP SUM wins by $100,000.00; lump-sum future value $265,329.77, total payments $0.00) there is nothing to compare. With a $0.00 lump sum (Present value $99,697.68, lump sum $0.00, difference $99,697.68 — ANNUITY wins by $99,697.68; lump-sum future value $0.00, total payments $160,000.00) the annuity wins by its whole present value. With a 10.00% discount rate (Present value $68,108.51, lump sum $100,000.00, difference -$31,891.49 — LUMP SUM wins by $31,891.49; lump-sum future value $672,749.99, total payments $160,000.00) the lump sum compounds to $672,749.99 and the annuity’s later payments are nearly worthless today. Rounding convention: every gap on this page is the difference of the displayed values: each side is rounded to cents first, then subtracted.

Output · formula · meaning

Who uses this

• The retiree offered $100,000.00 now or $8,000.00 a year for 20 years: they learn the lump sum wins by $302.32 at a 5.00% discount rate — and they check the 3.00% branch, where the annuity wins by $19,019.80.
• The lottery winner choosing cash or annual payments: they learn the discount rate is the whole comparison — and they check the tie rate, 4.96%, to see which side of the line their own return falls on.
• The worker offered a pension buyout: they learn $8,024.26 a year is the payment that makes the two exactly equal — and they check the $9,000.00 branch, where the annuity wins by $12,159.89.
• The saver comparing a lump sum invested at 5.00%: they learn the lump sum grows to $265,329.77 while the annuity pays $160,000.00 in total — and they check the 30-year branch, where the annuity wins by $22,979.61.

Accuracy & limitations

The math is first-principles: the present value of the annuity is A × (1 − (1+r)^−N) ÷ r, the lump-sum future value is L × (1+r)^N, and the total payments are A × N. Every figure is rounded to cents half-up, and every gap is the difference of the displayed values — each side rounded to cents first, then subtracted. What the model cannot do is make the decision for you: the discount rate is an assumption, and the whole answer turns on it — at 4.96% the two are tied, at 3.00% the annuity wins by $19,019.80, at 7.00% the lump sum wins by $15,247.89. Taxes are NOT modelled (a lump sum and annuity payments are often taxed differently — a real decision needs a tax adviser), inflation is NOT modelled (the annuity’s $8,000.00 buys less in year 20), the payments are assumed at the END of each year, and the annuity assumes the payer never defaults — a lump sum has no counterparty risk. Use this page to compare the two choices on the same numbers, then check the real offer — including its tax treatment and the payer’s credit — before you choose.

Frequently asked questions