Level Annual Premium Calculator

Work out level annual premium instantly with clear inputs, formula shown and shareable results.

About Level Annual Premium Calculator

The equivalence principle sets the present value of premiums equal to the present value of benefits: P = S·Aₓ / äₓ. Dividing by the annuity-due factor spreads the single premium over the premium-paying years; an expense loading then grosses it up.

Formula

Equivalence principle

P = S × Aₓ / äₓ; Gross = P / (1 - loading)

S: Sum assured
Ax: Assurance factor
äₓ: Annuity-due factor

Worked example

With the default values below, Level Annual Premium Calculator returns Level Net Annual Premium of $2,857.14. Change any input above and every figure here is recalculated in your browser.

Inputs used

Sum Assuredminimum 0: 250,000
Annual Mortality Rateaccepts 0.01–40 %: 1.2 %
Interest Rateaccepts 0.01–25 %: 5 %
Expense Loadingaccepts 0–80 %: 12 %

Results

Level Net Annual Premium: $2,857.14
Gross Premium After Loading: $3,246.75
Equivalent Net Single Premium: $48,387.10
Premium Annuity Factor äₓ: 16.9355 ×

Step by step

1Values used
2Equivalence principle
3Level Net Annual Premium= 2,857.14
4Gross Premium After Loading= 3,246.75
5Equivalent Net Single Premium= 48,387.10
6Premium Annuity Factor äₓ= 16.9355 ×

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 or tax into account.
Figures are rounded for display to 4 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 does the level premium exceed the pure yearly risk cost early on?

Because it is averaged over the whole contract. Early overpayments build the reserve that funds later years when mortality is higher.

How is the loading applied?

Dividing by (1 − loading) makes expenses a stated share of the gross premium, which is how office premiums are usually built.