£100,000, from contribution to income

Start with the income target

The calculation aims for the same nominal income each year. It first finds the initial cost of £1 at each payment date, allowing for investment risk and survival to release. Dividing the contribution by the sum of those forty costs gives the annual target.

The £7,420 figure is the certainty-equivalent target under ideal sharing, using the model’s investment assumptions and risk preference. The experiment then pays each rung’s full proceeds, so actual payments can be above or below that figure. Its simulated payments show the difference.

The target stays level in pounds. Its purchasing power would fall with inflation. The example uses hypothetical returns, synthetic mortality and no fees or tax; the full assumptions are recorded with the experiment.

Work back from a payment to its starting cost

Consider £1,000 at age 85. The investment policy gives £1 an estimated certainty-equivalent value of £2.1348 after twenty years. That is equivalent to 3.8646% a year, compounded. It reduces the opening investment to £468.44.

The model gives a 56.8% chance of reaching release at age 84. In the ideal pooling benchmark, the surviving members share the commitments of those who do not reach that date. The same £1,000 target can therefore begin with 56.8% of the investment-only amount.

This reduces the age-85 rung’s starting cost by 43.2%. The member receives that funding benefit by giving up beneficiary rights over money still committed to sharing. Both comparisons use the same investments.

The first rung releases immediately, so it has no sharing reduction. Later rungs rely more heavily on survivor allocations. Across all forty dates, the initial cost of a £1,000 annual target falls from £20,379 to £13,477, a 33.9% reduction under ideal sharing.

How investment risk and preferences determine the certainty-equivalent rate.

Divide the £100,000 between the rungs

The forty ideal-sharing costs sum to £13.477446 for £1 at every payment date. The contribution therefore supports an annual target of £100,000 ÷ 13.477446 = £7,419.80. Each rung’s opening investment is its cost per £1 multiplied by that target.

The first £7,165 releases immediately into the distribution account. The remaining £92,835 stays in longevity sharing. The first amount earns the model’s distribution-year return and pays £7,420 at age 66.

The two £100,000 allocations in the full table fund different targets. The sharing ladder allocates more to the early years to support its higher annual target, while distant rungs need less capital because of the expected survivor allocations.

Invest and share as the dates approach

Each rung follows its own investment timetable. Equity exposure is 80% at thirty or more years before release, falls gradually to zero at five years, and stays at zero through distribution. The age-85 rung begins with 44.8% in equities and 55.2% in bonds. It reaches an all-bond allocation at age 79.

Investment funds manage the assets. The sharing rule allocates account value among members of different ages and with different balances. The original investment stays in its rung. Each survivor allocation is invested across the recipient’s remaining rungs, using their dates, survival probabilities and remaining certainty-equivalent growth factors.

In this experiment, deaths are observed in order and each transfer is calculated and checked separately. The expected receipts and forfeited value must balance for each member under the mortality model. The fair-sharing explanation sets out that check. The later research on settling batches is a separate development.

Follow a recorded payment

The funding calculation sets aside £1,973.04 for age 85. To see what happens to it, take recorded history 174 from the 200-member experiment. It uses the same opening ladder and investment policy.

The original investment and its return supply £3,185.35 at release. Survivor allocations and their investment returns supply a further £2,393.55. Together they produce the £5,578.90 transferred to the distribution account at age 84.

One year’s growth at the model’s 3.5% continuous rate adds £198.72, producing a payment of £5,777.62. The member receives the whole amount. The experiment has no reserve to top it up to the target and retains no excess from larger payments.

Monthly income would require a different payment schedule and a corresponding funding calculation. This example makes one payment at the end of each distribution year.

How much do the payments vary?

The recorded account is one history. The 200-member experiment runs 1,000 histories with different investment returns and member lifetimes. The closed pool starts with members aged about 55–80 and balances of £60,000–£140,000. Members experience the same modelled equity-market shocks, while lifetimes are independent. All 575 histories in which the member reaches age 84 complete that rung’s release.

The median sharing payment is about £7,592. Giving greater weight to low outcomes reduces its certainty equivalent to about £7,437, close to the £7,420 funding target. These are conditional age-85 results. Each year’s distribution is assessed separately.

At age 105, only 18 histories reach the required release age; two have already encountered a pool stop. The chart therefore leaves that result blank. A stopped history retains an account balance, but the experiment does not assign its eventual settlement or payment.

Over the full sharing horizon, 153 of the 1,000 pool histories stop. This can happen after the example member’s life has ended or after many of their rungs have released. Pool continuation and that member’s completed payments are therefore separate counts.

Compare all three pool sizes, their outcomes and the recorded stopping reasons.

What belongs to the member and their beneficiaries?

Release changes the rights attached to the money. It is recorded separately from payment, even though the released assets continue to earn an investment return.

The recorded account also illustrates beneficiary rights. The member reaches the final release at 104, then their life ends before the payment at 105. That final rung has already left sharing, so its £10,358.57 payment goes to the beneficiary.

Who holds the assets, administers the accounts and verifies the instructions.

The decisions needed to complete the pension

The example specifies an opening allocation, investment policy, transfer rule and payment calculation. Completing the pension requires the following decisions to be made and tested together.

Continuation and settlement

Choose how committed assets are supported or settled when the existing pool cannot continue, including cases where another pool cannot accept them. Then integrate the batch and continuation rules into the payment simulation.

Payments and any retained reserve

Compare the full-proceeds rule with smoothing or minimum-income policies. Define who owns any retained assets and how a shortfall is funded.

Admissions and later contributions

Specify entry across the remaining ladder and test whether both existing and new commitments can be supported.

Income beyond the final rung

Provide for lives extending beyond the example’s last payment at 105, and value that provision in the initial contribution.

Investment and operating arrangements

Include investment costs, inflation and market stresses; establish valuations, evidence requirements and responsibilities for disputes or provider closure.

Once those rules determine the remaining outcomes, the full payment distribution can be used to revisit the opening investments. Preferences across years, other pension income and provision for beneficiaries belong in that assessment.

The next integrated research study.

The calculation record

The figures on this page use the experiment of 7 September 2026. The funding schedule and payment accounts are shared with the simulation pages.

All forty opening amountsOutcome statistics and coverageThe recorded accountMethodComplete source archive