Under the formula method actuarial formulas are used. The fundamental principle in the equation of value is that:
The present value of premium (Receipts) = Present Value of Benefits (Outgo) + Present Value of Expenses (Outgo).
Actuarial formula makes the use of commutation functions which take into account the probability of death and survival along with discount rates. Usually a life table is used in which we have the age x, the number of survivors at age x and the number of deaths from exact age x to exact age x+1.
Premium payable for a life at entry age x every year as long as he is alive = (The present value of benefit payable on the death of survivor at any age after x) / ( The present value of benefits payable every year to a life aged x as long as the life is alive)
Premium payable for a limited period of n years = (The present value of benefit payable on the death of survivor at any age after x) / ( The present value of benefit payable every year to a life aged x as long as the life is alive before age x+n )
Term Assurance Contracts:
Premium payable every year for n years = {(The present value of benefits payable on death at any age after x but before x+n) + ( The present value of benefits payable on survival at age x+n)}(The present value of benefits payable every year to a life aged x as long as the life is alive before age x+n)
A simple premium payable only once as a lump sum at the beginning of the policy = (The present value of benefits payable on death at any age after x but before x+n) + ( The present value of benefits payable on survival at age x+n)
Pure Endowment Contracts:
Premiums payable every year for n years =(The present value of benefits payable on survival at age x+n)/ (Present value of benefits payable every year to a life aged x as long as the life is alive before age x+n)
A single premium payable only once as a lump sum at the beginning of the policy = The present value of benefits payable on survival at age x+n
Endowment Assurance Contracts:
Premiums payable every year for the n years of the contract = (The present value of benefit payable on death after the commencement of the policy before n years)/( The present value of benefit payable every year to the insured life as long as the life is alive for n years of the contract.)
A single premium payable = The present value of benefit payable on death after the commencement of the policy before n years)
The present value of premium (Receipts) = Present Value of Benefits (Outgo) + Present Value of Expenses (Outgo).
Actuarial formula makes the use of commutation functions which take into account the probability of death and survival along with discount rates. Usually a life table is used in which we have the age x, the number of survivors at age x and the number of deaths from exact age x to exact age x
Premium payable for a life at entry age x every year as long as he is alive = (The present value of benefit payable on the death of survivor at any age after x) / ( The present value of benefits payable every year to a life aged x as long as the life is alive)
Premium payable for a limited period of n years = (The present value of benefit payable on the death of survivor at any age after x) / ( The present value of benefit payable every year to a life aged x as long as the life is alive before age x+n )
Term Assurance Contracts:
Premium payable every year for n years = {(The present value of benefits payable on death at any age after x but before x+n) + ( The present value of benefits payable on survival at age x+n)}(The present value of benefits payable every year to a life aged x as long as the life is alive before age x+n)
A simple premium payable only once as a lump sum at the beginning of the policy = (The present value of benefits payable on death at any age after x but before x+n) + ( The present value of benefits payable on survival at age x+n)
Pure Endowment Contracts:
Premiums payable every year for n years =(The present value of benefits payable on survival at age x+n)/ (Present value of benefits payable every year to a life aged x as long as the life is alive before age x+n)
A single premium payable only once as a lump sum at the beginning of the policy = The present value of benefits payable on survival at age x+n
Endowment Assurance Contracts:
Premiums payable every year for the n years of the contract = (The present value of benefit payable on death after the commencement of the policy before n years)/( The present value of benefit payable every year to the insured life as long as the life is alive for n years of the contract.)
A single premium payable = The present value of benefit payable on death after the commencement of the policy before n years)
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