Question

a 40-year-old person wants to purchase a $200,000 one-year life insurance policy. what should the insurance company charge the person for the policy if it wants an expected profit of $50?
age | probability of death
20 | 0.00040
30 | 0.00070
40 | 0.00090
50 | 0.00315
the company should charge the person $

Explanation:

Step1: Define Variables

Let \( x \) be the premium charged. The insurance company pays out $200,000 if the person dies (probability LXI1) and keeps the premium LXI2 if the person survives (probability LXI3). The expected profit is $50.

Step2: Set Up Expected Profit Equation

The expected profit \( E \) is calculated as:

$$ E = (x - 200000) \times 0.00090 + x \times 0.9991 $$

We know \( E = 50 \), so:

$$ 50 = (x - 200000) \times 0.00090 + x \times 0.9991 $$

Step3: Expand and Simplify

Expand the equation:

$$ 50 = 0.00090x - 180 + 0.9991x $$

Combine like terms:

$$ 50 = (0.00090 + 0.9991)x - 180 $$

$$ 50 = x - 180 $$

Step4: Solve for \( x \)

Add 180 to both sides:

$$ x = 50 + 180 $$

$$ x = 230 $$

Answer:

230