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