To determine the premium that the insurance company should charge a 50-year-old person for a \[tex]$200,000 one-year life insurance policy, we need to account for the expected payout based on the probability of death and add the desired profit.
1. Insurance Policy Value: The insurance policy is valued at \$[/tex]200,000.
2. Expected Profit: The insurance company wants an expected profit of \[tex]$80.
3. Probability of Death: The given probability of death for a 50-year-old person is 0.00325.
First, we'll calculate the expected payout. The expected payout can be found by multiplying the value of the insurance policy by the probability of death:
\[
\text{Expected Payout} = \text{Insurance Policy Value} \times \text{Probability of Death} = \$[/tex]200,000 \times 0.00325
\]
Calculating this:
[tex]\[
\text{Expected Payout} = \$200,000 \times 0.00325 = \$650.00
\][/tex]
Next, we need to add the expected profit to the expected payout in order to determine the premium that the person should be charged:
[tex]\[
\text{Premium} = \text{Expected Payout} + \text{Expected Profit} = \$650.00 + \$80
\][/tex]
Calculating this:
[tex]\[
\text{Premium} = \$650.00 + \$80 = \$730.00
\][/tex]
Therefore, the insurance company should charge the person [tex]\( \$730 \)[/tex] for the one-year life insurance policy to achieve the expected profit of \$80.
