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# Annual Premiums to be charged by an insurance company

The manager of a life insurance company is trying to decide what annual premium to charge a group of policyholders, each of whom has just received his or her 40th birthday. A check of mortality tables indicates that, for every million persons born 40 years ago, 3percent die, on average, sometime during their 40th year. If the company has 10,000 policyholders in this age bracket and each has taken out a \$50,000 life insurance policy, estimate the probable amount of death benefit claims against the company.

How much must be charged in premium from each policyholder just to cover these expected claims?

Suppose the company has operating expenses (plus a target profit) on sales to these policyholders of \$500,000. What annual premium must be charged each policyholder to recover expenses and meet expected benefit claims?

#### Solution Preview

To calculate the premium amount for life insurance, three types of information are required:

Costs
Interest
Mortality

Costs:

We are given costs and mortality in the problem. The costs are designed to include all costs of operations such as salaries, rent, commissions, death benefits and profit. The premium amounts can be computed much as product prices in other industries. Costs are the easy part of the insurance industry because they are much like other businesses.

How much must be charged in premium from each policyholder just to cover these expected claims?

The amount that must be charged to cover only the expected claims is given in the problem:
10,000 policyholders * 3% will die in their 40th year = 300 insured policyholders
If each policy has a face value of \$50,000 * 300 = \$15,000,000 will be paid out.
There are 10,000 policyholders to cover the expected claims. The annual premium would be 15,000,000 / 10,000 = \$1500 per year per ...

#### Solution Summary

The three components required to calculate the amount of life insurance premiums are explained in the solution. References are provided.

\$2.19