Background BACKGROUND

An insurance company is considering the introduction of an investment-only product that provides a claim based on the accumulated value of premiums paid by a policyholder. Policyholders would pay annual premiums of X at Year 0, 1, 2, …, n-1 and would receive a claim equal to the accumulated value of the premium payments at Year n . Unless told otherwise, for the following questions use an interest rate of 4% per annum and assume that . Assume also that, for the moment n=25, and until told otherwise, policyholders do not die during the 25 year policy period.

A policyholder is wishing to receive a claim payment of $300,000. Calculate the value of the premium payment (to 2 decimal places), that will provide this claim payment.