Question

An actuary at a life insurance company is working on a project to see if the life insurance company has collected enough premiums to pay projected life insurance claims. His calculations show that the company will have a liability due in 10 years in the amount of $53,250,000. In other words, the actuary calculations estimate that the life insurance company will receive claims in the amount of $53,250,000 in 10 years based on life probability estimates of its clients. The life insurance company will need to have $53,250,000 in 10 years to pay out its projected claim obligations. To date, the life insurance company has collected $35,000,000 in premium payments. It is standard procedure to use an investment grade corporate bond rate to discount the liability claim to the present value and then compare the present value of the liability amount to the premiums collected, then the firm is projected to have collected enough premium payments. The investment grade corporate bond rate is 3.75%.

A. Calculate the present value of the liability due in 10 years. $____________

B. Has the life insurance company collected enough in premium payments to pay for the liability in 10years?

Yes or No?

Answer 1

A.

The present value of the liability due = discounted value of liability due = expected Liability due / (1+investment rate)^10

= 53,250,000 / (1+3.75%)^10

=$ 36,850,090

B. As the Present value of liability due is more than the collected premium of $35,000,000, so the company has Not collected enough premiums.