Pension Lump Sum vs Annuity Calculator

Pension Lump Sum vs Annuity Calculator

Offered a lump sum or a pension for life? See the payout rate the pension implies, how long it takes to pay back the lump sum, what the pension is worth today, and the return the lump sum would need to match it.

Value of the pension today

Lump sum vs pension → present value
A planning age, not an average. Life tables give averages; about half of people outlive them, so plan beyond.
Also the rate used to value the pension today. A safe, taxable deposit rate is the fair comparison for a guaranteed pension.
Defaults to your currency’s central-bank target (India 4%, US/UK/Euro/Canada 2%). Actual inflation often runs higher — try 5–6% for a cautious plan. For AED, SAR, PKR, BDT and MYR there is no official target: enter your own estimate.
$28,85,496Example

$30,00,000 lump sum, or $20,000 a month fixed for life; age 60, planning to 85; 7% return

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Present value of the pension and the break-even return

PV = P × a12 × [1 − qN] ÷ (1 − q); q = (1 + g) ÷ (1 + r); a12 = [1 − (1 + i)−12] ÷ i; i = (1 + r)1/12 − 1
P
the monthly pension, paid at the end of each month
g
the yearly rise in the pension: inflation if indexed, 0 if fixed
r, i
the annual return (effective) and its monthly equivalent
N
years from your age now to the planning age
break-even return
the r at which PV equals the lump sum, found by bisection; above it the lump sum wins, below it the pension

Worked example

$30,00,000 lump sum, or $20,000 a month fixed for life; age 60, planning to 85; 7% return
Payout rate: 20,000 × 12 ÷ 30,00,000 = 8.00% a year; months to equal the lump sum: 150
Monthly rate i = 1.071/12 − 1 = 0.5654%; a year of pension is worth 20,000 × 11.5704 at its start
PV = 20,000 × 11.5704 × (1 − 1.07−25) ÷ (1 − 1 ÷ 1.07) = $28,85,496
That is $1,14,504 less than the lump sum: the lump sum needs only 6.55% a year to pay the same pension to 85
Paying the pension from the lump sum at 7% leaves $6,21,460 at 85
If the pension rose 4% a year with prices, it would be worth $41,99,577 and the lump sum would run out by 76
The last year's $20,000 is worth $7,802 a month in today's money at 4% inflation

Lump sum or pension: how to compare them

A pension scheme, an employer or an insurer may offer a choice: a lump sum now, or a monthly pension for life. The two are not directly comparable, because one is money today and the other is a stream of payments whose total depends on how long you live. This page puts them on the same footing in four ways.

Payout rate. The pension a year as a share of the lump sum: $20,000 a month for $30,00,000 is 8% a year. It is not an interest rate — part of each payment is your own capital coming back — but it lets you compare offers. Simple payback. The lump sum divided by the monthly pension: 150 months, twelve and a half years. Value today. What the pension payments to your planning age are worth now, discounted at the return you could earn — $28,85,496 in the example at 7% to age 85, a little less than the lump sum. Break-even return. The return the lump sum would have to earn to pay the same pension until the planning age: 6.55% a year here. If you can reliably earn more, the lump sum wins; if not, the pension does. The chart shows the same thing year by year: the lump sum, invested at your return and paying out the pension, against the pension received. At 7% the lump sum pays the fixed pension to 85 and still has $6,21,460 left — but a fixed pension is the weaker offer; see inflation below.

How long to plan for. The answer turns on the planning age. The Registrar General’s SRS abridged life tables give the average remaining life at each age for India, but an average is a poor plan: roughly half of people outlive it, and a pension’s main value is that it keeps paying however long you live. Try your planning age a few years either side and see whether the verdict flips. A lump sum, unlike a life pension, can be left to your family if you die early — check whether the pension has a spouse’s pension or return of purchase price, which changes the comparison.

Inflation. A fixed pension loses buying power: at 4% inflation, the $20,000 paid at 84 buys what $7,802 buys today. Choose “rises with prices” if the pension is indexed; the value today is then $41,99,577 and the break-even return 10.57% — the verdict flips, and the pension wins. A government pension with dearness relief is indexed; most private annuities are not.

How this differs from the annuity payout calculator. The annuity payout calculator starts from a price you pay an insurer and shows the income an annuity rate buys. This page starts from two offers already on the table and tells you which is worth more on your assumptions. Tax: a pension is taxed as income each year; the tax on a lump sum depends on the scheme, so compare after-tax figures where you can. For drawing an income from a lump sum yourself, see the SWP calculator; for discounting any future sum, the present value calculator. This is arithmetic on the figures you enter, not financial advice.

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Frequently asked questions

Should I take the lump sum or the pension?

Compare the pension’s value today with the lump sum, and the return the lump sum would need to match the pension to your planning age with what you can safely earn. The longer you expect to live and the lower safe returns are, the better the pension looks.

What is the break-even age for a pension?

Without investment returns, the lump sum ÷ the monthly pension: $30,00,000 ÷ $20,000 = 150 months. Allowing for returns it is later: at 7% the invested lump sum pays a fixed $20,000 to 85 with money left; for a pension rising 4% a year it runs out by age 76.

How is the implied annuity rate worked out?

The yearly pension ÷ the lump sum: 2,40,000 ÷ 30,00,000 = 8%. It includes the return of your own capital, so it is not comparable with a deposit interest rate.

Does inflation change the answer?

Yes. A fixed pension loses buying power each year, while an indexed one keeps it. Choose whether your pension rises with prices; the page values it with the yearly increases included.

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References

  1. Brealey RA, Myers SC, Allen F. Principles of Corporate Finance. McGraw-Hill. Present value of an annuity and of a growing annuity; the internal rate of return.
  2. Office of the Registrar General & Census Commissioner, India. SRS Based Abridged Life Tables (latest 2019–2023): expectation of life at each age for India and the larger states, by sex and residence. An average, not a plan — about half of people live longer than it.
  3. Central-bank inflation targets used as default inflation by currency: Reserve Bank of India (4% CPI, flexible inflation targeting framework); U.S. Federal Reserve (2% PCE); European Central Bank (2%); Bank of England (2% CPI); Bank of Canada (2%); Reserve Bank of Australia (2–3%); Bangko Sentral ng Pilipinas (3% ± 1). Actual inflation often runs above target.