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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, 1,2,3…, n-1 and would receive a claim equal to a the accumulated value of the premium payments at Year n. Unless told otherwise, for the following questions use an interest rate of 4 percent per year and n=25.
1. Calculate the present value, at Year 0, of a single premium payment of $5,000 made at Year 12.
2. Calculate the accumulated value, at the time that the claim is paid, of all of the premium payments of $5,000.
3. A policyholder is wishing to receive a claim payment of $300,000. Calculate the value of the premium payment X, that will provide this claim payment.
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