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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.
Equivalence principle
P = S × Aₓ / äₓ; Gross = P / (1 - loading)
Figures are estimates for planning only. Rates, mortality and market assumptions change. This is not financial, actuarial or tax advice.
Because it is averaged over the whole contract. Early overpayments build the reserve that funds later years when mortality is higher.
Dividing by (1 − loading) makes expenses a stated share of the gross premium, which is how office premiums are usually built.