A 50-year-old person wants to purchase a [tex]$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 $[/tex]80?

| Age | Probability of Death |
|-----|-----------------------|
| 20 | 0.00070 |
| 30 | 0.00070 |
| 40 | 0.00090 |
| 50 | 0.00325 |

The company should charge the person $ ______.



Answer :

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.