A financial institution has issued a large number of 20-year policies. Under these policies: Premiums are payable annually in advance. A maturity benefit of Rs 10,000 is payable at the end of 20 years. Premiums are calculated such that the present value of benefits payable and expenses incurred equal that of the premiums under the policies. In doing this calculation, the financial institution makes the following assumptions: Interest 5% per annum effective, Expenses at the start of the policy 2% of the maturity benefit, Ongoing expenses 3% of each premium paid. (a) Calculate the annual premium for each of these policies assuming that premiums under all policies continue to be paid for each of the 20 years. (b) The financial institution observes that on each premium due date, 4.5456% of the policies that had paid premiums in the preceding year, defaulted on their premiums. It has been decided that policies that defaulted in premiums would be immediately refunded the premiums already paid under them, without any interest. Also, they would not be eligible for the maturity benefit of Rs 10,000. The financial institution wishes to recalculate the premiums for these policies to allow for these premium defaults. Calculate the revised annual premium. HOW TO SOLVE PART (B)?
