What this calculator does
A deferred annuity pays nothing for a set period, then pays regularly for a set term. Pensions work this way, as do many retirement products: contributions accumulate, then a payout stream begins years later.
Deferral costs a great deal in present value terms. A stream worth $118,503.51 at the moment payments begin is worth $87,855.21 today if that moment is five years away, and only $35,799.45 if it is twenty years away.
The formula
The annuity is valued first as an ordinary annuity at the moment payments begin, then discounted back across the deferral period at the same periodic rate.
| Term | Meaning |
|---|---|
| Deferral period | The years before payments start, during which nothing is received. |
| Value at the start of the payout | What the stream is worth on the day payments begin. |
| Present value today | That figure discounted back across the deferral period. |
The inputs explained
| Field | What to enter |
|---|---|
| Payment per period ($) | The payment received each period once payments begin. |
| Annual interest rate (%) | The annual interest rate. |
| Payments per year | Payments per year. |
| Deferral period before payments start (years) | Years before payments start. |
| Years payments continue for | How many years the payments continue for. |
When to use it
Valuing a pension entitlement
A pension starting at 65 is a deferred annuity, and its value today depends heavily on how far off that is.
Comparing a lump sum against a future income
An offer to take cash now can only be judged against the present value of the stream given up.
Planning a retirement income
Working backwards shows what needs accumulating now to fund a payout starting later.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How much does deferral reduce the value?
The same payout stream starting at four different points.
| Deferral period | Present value today | Value at the start of the payout period |
|---|---|---|
| Starts now | $118,503.51 | $118,503.51 |
| 5 years | $87,855.21 | $118,503.51 |
| 10 years | $65,133.41 | $118,503.51 |
| 20 years | $35,799.45 | $118,503.51 |
Questions
Why does deferral reduce the value so much?
Because discounting compounds. At 6 per cent, money twenty years away is worth about 30 per cent of its face amount today, so the same stream loses roughly 70 per cent of its present value simply by starting later.
Is this how pensions are valued?
The structure is the same, but an actual pension valuation also accounts for mortality, indexation and the possibility of not living to claim. This gives the financial skeleton rather than the full actuarial figure.
What discount rate should be used?
Something reflecting the certainty of the payments. A government pension warrants a low rate close to government bond yields; a promise from a company with uncertain prospects warrants a higher one.
Does the accumulation phase matter here?
Not to this calculation, which values the payout stream only. Whether contributions are being made during the deferral period is a separate question, handled as its own annuity.
For payments starting immediately, see the annuity due calculator. For a stream that grows each period, see the growing annuity calculator.