Complete information on Retrospective Method of calculating Reserve

Under this method, the reserve is derived entirely by reference to past experience. The reserve represents the net premiums collected by the insurer for a particular class of policies plus interest at an assumed rate, less the death claims paid out.

We calculate for each year how much would have been received by way of premiums on the basis of assumed mortality figures, how much interest would have been earned on the basis of assumed interest rate and how much would have been paid by way of claims on the basis of assumed mortality figures.

Group Approach :

The calculation begins with the first year when the total net premium has been received for the first time. We, then, determine the amount of interest that this total of net premium receipts will earn for one full year at the assumed rate of interest.

For the total of these two claims paid for the first year are deducted to get the reserve. Again in the second year, we carry forward the reserve.

The net premium received from the surviving policyholders is added to the reserve of past year which is taken together and is called initial reserve of the second year. This process continues until all the policyholders are dead or policy period expires.

Per policy reserve can be calculated by dividing the total reserve by the number of policies. It can be illustrated with the following formula.

For example, there are 10 policyholders insured for Rs. 10,000 each for the period of 10 years. They are required to pay net premium of Rs. 1,000 each. The rate of interest is 10 per cent per annum.

Reserve in a Particular Year:

The reserve at a particular time can be calculated by the following formula- Reserve = Reserve at the close of the previous year (if any) + Premium of the Year.

Interest thereon at the assumed rate for one year – Claims for the year

With this help reserve can be calculated at any moment provided the initial reserve is known.

Another Method on Accumulation Basis:

The accumulated value of premiums over the accumulated value of claims will be the retrospective reserve.

Reserve = Accumulated value of Past Premiums

Accumulated value of Past Claims

The accumulated value is calculated on the basis of assumed death rate per year and assumed rate of interest. The accumulation factors can be known from the interest table. Thus, the calculation is simple in this method.

Individual Approach:

The retrospective reserve may also be calculated on every policy. The method of calculation is the same as discussed above with only difference that the reserve will be calculated on the basis of cost of insurance instead of claims paid on.

The ‘cost of insurance’ reveals how much amounts will have to be shared by the policyholders in payment of claims of other policy-holders.

Technically, the prorate share of death claims in any particular year is called the ‘cost of insurance’. It is the amount which must be paid for the protection.

The cost of insurance is arrived by multiplying amount at the risk with the probability of death to him. The amount at risk is the amount which is obtained by deducting the initial reserve of the policy-holders from the policy amount. In brief-

Cost of Insurance =Amount at risk x Probability of Death.

= (Policy Amount-Initial Reserve) x Probability of death.

The individual reserve can be explained by an illustration. For example, a policyholder takes policy of Rs. 10,000 (for ten years) and pays Rs. 1,000 an annual premium, the rate of interest being 10 per cent. The probability of death in the first year is 0.002 and in the second year 0.003. We have to calculate reserve for two years.

Difference between Group Reserve and Individual Reserve:

1. The group reserve increases up to a point of time and decreases thereafter until it is finished completely. The individual reserve increases each year and in the end it becomes equal to the policy amount.

2. The group reserve will be zero when payments of claims of all the policy-holders are made whereas the individual reserve must be equal to the face value of the policy at the maturity.