i need help with this :))))

Question

Miranda decided to buy a $50,000 term life insurance policy from Palmetto Insurance Company to cover her until she is 55. She is currently 50 years old and in good health. The probability of death in a given year is provided by the Social Security Actuarial Life Table. 

x=x= Age	50	51	52	53	54
PP(Death at a Given Age)	0.0032	0.0035	0.0038	0.0041	0.0044

1. Fill in the expected cost to Palmetto Insurance Company for each year Miranda has the policy.

Age at Death	50	51	52	53	54
Expected Cost	$ ?	$ ?	$ ?	$ ?	$ ?

2. The insurance company wants to make a profit of $500. How much would they need to charge for the policy? $__________

Answer 1

This is a typical expected value problem, E(X) = sum(f(X)*X) in a different wrapper.

Some assumptions:

1. You do not need to deal with the profit the company makes each year that the customer did not die
2. The customer can, of course, die only once.

So, the expected cost to the company for each year of the policy is obtained by multiplying the probability of dying by the value of the policy. For instance, the expected cost of the policy in its first year when the customer is 50 is f(x)*X = (.0032)*50,000 = $160.00. I'm assuming the company wants to make at least $500.00, not exactly $500.00. The potential expected cost to the company increases with each passing year that the customer remains alive. So the worst-case scenario is the cost when the customer is 55.

Simply add $500 to that cost, and you have the total price the company should charge the customer.