An insurance company wants to offer a 3 year term insurance contract to a male aged...

An insurance company wants to offer a 3 year term insurance contract to a male aged 70. This contract pays $1M at the end of the year of death if death occurs during the first three years. Premiums are paid at the beginning of each year. Assume r=.02 (annual compounding), and that one year probabilities of death at age 70, 71 and 72 are 0.024, 0.026, 0.028. What is the minimum annual premium?

Solutions

Expert Solution

The present value of the 3 year pay offs is shown below. Pay off for each year is calculated by multiplying $1M with probability for that year.

Let P be the annual premium. For minimum annual premium, PV of all premiums must be equal to PV of expected pay offs.

PV of premiums is calculated as shown below

Equating both PVs,

2.941561P = $74,905

P = $25,464

Minimum annual premium is $25,464

jeff jeffy answered 2 years ago

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