Actuarial Present Value of Benefit (APV of benefit) means the expected present value of the benefit payment.

If the insurer sets its premium (the price or cost) as the expected benefit payment, it is called the equivalence principle.

When the equivalence principle is used to determine a single premium, the premium is equal to the APV of the benefit payments and is called single benefit premium (SBP).

Under the equivalence principle, benefits premium is determined by

E (PV of benefits premium) = E (PV of benefit)

SBP = APV of benefit

The actual premium charged to the customers at the time 0 will be APV plus others charges e.g. sales commission, profit, tax, etc.

Obviously, APV of benefit is a function of insured's age (X) and types of insurance involved.