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Reserve At Time T Calculator

Work out reserve at time t instantly with clear inputs, formula shown and shareable results.

About Reserve At Time T Calculator

A reserve is the fund an insurer must hold so that future premiums plus the fund cover future claims. The recursion ₜ₊₁V = [(ₜV + P)(1 + i) − q·S] / p rolls the fund forward one year: add the premium, credit interest, pay expected claims and spread the balance over survivors.

Formula

Reserve recursion

(ₜV + P)(1 + i) = q·S + p·ₜ₊₁V

V
Reserve
P
Premium
i
Interest
q
Mortality
S
Sum assured

Worked example

With the default values below, Reserve At Time T Calculator returns Policy Reserve At Time t of $11,883.18. Change any input above and every figure here is recalculated in your browser.

Inputs used

Annual Premium Per 100,000 Sum Assuredminimum 0
1,800
Interest Rateaccepts 0.01–25 %
5 %
Annual Mortality Rateaccepts 0.01–40 %
1 %
Years Elapsed (t)accepts 1–60
10

Results

Policy Reserve At Time t
$11,883.18
Accumulated Premiums
$22,640.21
Accumulated Expected Claims
$12,577.89
Reserve As % Of Sum Assured
11.883%

Step by step

  1. 1Values used
  2. 2Reserve recursion
  3. 3Policy Reserve At Time t= 11,883.18
  4. 4Accumulated Premiums= 22,640.21
  5. 5Accumulated Expected Claims= 12,577.89
  6. 6Reserve As % Of Sum Assured= 11.883

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax or fees or charges into account.
  • Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
  • Figures are estimates for planning only. Rates, mortality and market assumptions change. This is not financial, actuarial or tax advice.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Figures are estimates for planning only. Rates, mortality and market assumptions change. This is not financial, actuarial or tax advice.

Frequently Asked Questions

Why divide by the survival rate?

The fund left after paying claims belongs to the survivors only, so it is shared among a smaller group.

Can a reserve be negative?

Early on it can be, if the premium is back-loaded. Regulators normally floor reserves at zero for solvency reporting.

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