A universal life policy provides a death benefit at the end of the period of death of 100 000. The account value at time 20 is 2500. For the time period from time 20 to time 21, the credited interest rate is 0.006, the expense charge is 5% of any premium paid plus 100, and the cost of insurance rate is 30 per thousand.
(a) Suppose that at time 20, the policyholder makes the minimum premium payment of 500, which according to the guarantee in the contract ensures that the cost of insurance will be paid regardless of the amount in the account. Find the account value at time 21.
(b) If the contract does not carry the secondary guarantee of part (a), what is the minimum premium that the policyholder will have to pay at time 20 to ensure that the cost of insurance can be paid.