Longevity Risk Calculator (extra money for living longer)

Understanding the longevity risk calculator — concept and principle

Longevity risk is the risk of living longer than your money lasts. Plans built to "average" life expectancy fail for roughly half of people, who outlive the average. This calculator puts a price on that risk. It compares the savings needed to fund your spending until your planned life expectancy with the savings needed to fund it until a later "safety" age, and shows the extra amount required to close the gap.

How it is calculated

Each year's spending is treated as a payment made at the start of the year (an annuity due), and all payments are discounted back to your retirement date at the real (after-inflation) return r.

• Years to fund: n = end age − retirement age.
• Savings needed: PV = S × (1 − (1 + r)^−n) ÷ r × (1 + r), where S is annual spending in today's money.
• If r = 0, PV = S × n.
• Extra savings = PV(safety age) − PV(planned age); Increase = PV(safety) ÷ PV(planned) − 1.

The principle

Money you will spend in year 25 does not need to be fully set aside today: it can earn a return in the meantime. Discounting each payment by (1 + r)^t tells you how much you need now. The formula above is simply the sum of those discounted payments. Distant years are discounted most, so ten extra years cost less than ten years of spending, but far from nothing.

Worked example

Default inputs: spending $40,000 a year, retirement at 65, planned life expectancy 85, plan for age 95, real return 3%.

1. Planned horizon n = 85 − 65 = 20 years: PV = 40,000 × (1 − 1.03^−20) ÷ 0.03 × 1.03 = $612,952.
2. Safety horizon n = 95 − 65 = 30 years: PV = 40,000 × (1 − 1.03^−30) ÷ 0.03 × 1.03 = $807,538.
3. Extra savings needed = 807,538 − 612,952 = $194,586 to fund ages 85–95.
4. Increase = 807,538 ÷ 612,952 − 1 = 31.7%.

How to read the result

The extra amount is the cost of "insuring yourself" against a long life using your own savings. A lower real return makes the gap bigger, because less growth helps pay for distant years. If the figure seems unreachable, compare it with guaranteed lifetime income: a life annuity or delaying a public pension shifts longevity risk to an insurer or the state, often more cheaply than self-funding the tail.

Common mistakes

• Using a nominal return together with today's spending, which overstates what your savings can do.
• Planning to average life expectancy at birth instead of life expectancy at your current age, which is higher.
• Ignoring pension income: enter only the spending your savings must cover.

Frequently asked questions

What age should I plan for?

Many planners use an age you have only a small chance of outliving, such as 95 or 100, rather than the average.

Does a higher real return reduce longevity risk?

It lowers the cost of the extra years, but higher expected returns come with more volatility, so they do not remove the risk.

Sources: Society of Actuaries and American Academy of Actuaries, Longevity Illustrator · Brealey, Myers and Allen, Principles of Corporate Finance (annuity present value)