Question

The XYZ Casualty Insurance Company has found that for a particular type of insurance policy it makes the following payments for insurance claims: i) On 10% of the policies, XYZ Company pays $1,000 exactly one year after the effective date of the policy. ii) On 3% of the policies, XYZ Company pays $10,000 exactly three years after the effective date of the policy. iii) On the remaining policies, XYZ Company makes no payment for claims. In addition to the above payments, XYZ Company pays $20 for the expenses of administering the policy: $10 is paid on the effective date of the policy and the remaining $10 is paid six months after the effective date of the policy. The annual interest rate is 8%, compounded semiannually. The premium for this type of insurance policy is due six months after the effective date of the policy. If the present value of the premium is set equal to the present value of the claim payments and expenses, what is the premium?
(A) Less than $355
(B) At least $355 but less than $380
(C) At least $380 but less than $415
(D) At least $415 but less than $440
(E) At least $440

Answer 1

Answer:

(B) At least $355 but less than $380

Explanation:

i. Claim payments to be made

$1000 to be paid after one year of the policy

So, Present value of $1000 at 8% semi-annually = $1000/(1.04^2)) = $924.56

10% of this policy is paid = $924.56*10%= $92.46

ii. Claim payments to be made

$10000 after 3 years

So, present value= $10000/(1+0.08/2)^6 =$10000/1.046 = $7,903.14

3% of this policy claim are payable after 3 years= $7903.14* 3% = $237.09

iii. Administration expenses = $20

$10 on the effective date

$10 after 6 months

So, present value of $10 after 6 months= $10/(1.04)= $9.62

Total present value of expenses to be made by the company = $92.46 + $237.09 + $10 + $9.62 = $349.17

As the present value of the premium is set equal to the present value of the claim payments and expenses. Then, the present value of the premium is equals to $349.17.

The actual cost of the premium paid in 6 months = $349.17*1.04 = $363.14. So the option B is correct.