Question

There is a 0.99967 probability that a randomly selected 26 -year-old female lives through the year. An insurance company wants to offer her a one-year policy with a death benefit of $700,000. How much should the company charge for this policy if it wants an expected return of $300 from all similar policies? The company should charge $ (Round to the nearest dollar.)

Answer 1

To determine how much the insurance company should charge for the one-year policy with a death benefit of $700,000, they need to consider the probability of the policyholder's survival and the expected return.

Let's break down the problem step by step:

1. The probability of the 26-year-old female surviving the year is 0.99967.

2. The expected return from all similar policies is $300.

3. The death benefit of the policy is $700,000.

To calculate the premium the company should charge, we can set up an equation based on expected value:

Expected Value = (Probability of Survival * Premium) - (Probability of Death * Death Benefit)

Expected Value = (0.99967 * Premium) - (0.00033 * $700,000)

Now, we want the Expected Value to be $300:

$300 = (0.99967 * Premium) - (0.00033 * $700,000)

Now, let's solve for Premium:

$300 = 0.99967 * Premium - 231

Add 231 to both sides:

$300 + 231 = 0.99967 * Premium

$531 = 0.99967 * Premium

Now, divide both sides by 0.99967 to find the Premium:

Premium = $531 / 0.99967

Premium ≈ $531,355 (rounded to the nearest dollar)

So, the insurance company should charge approximately $531,355 for this policy if they want an expected return of $300 from all similar policies.