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2.2 In order to match asset income to the liabilities in Example 7.5 so that PVA(.10)=PVL(.10), a level annual payment annuityimmediate with n payments is purchased to provide the asset income flow. For each of n=5,15,50,100, find the required annual payment and calculate both tAtv.10t and t2Atv.10t. Which value of n provides the nearest match to the relation tAtv.10t=tLtv.10t ? Solve for the exact value of n for which tAtv.10t=tLtv.10t. Determine whether this provides Redington immunization for the portfolio. (Exact matching of assets and liabilities) A small company terminating its operations has decided to provide each of its three employees with a severance package that pays 10,000 per year (at the end of each year) up to and including at age 65 , plus a lump sum payment of 100,000 at age 65 . In case of death of an employee before age 65 , the payments continue until that employee would have been 65 . The three employees are now exact ages 50, 53 and 55 . The company determines that the payments due under this package can be met by the income and maturities generated by three bonds, each with a face amount of 100,000 and an annual coupon rate of 10% and with maturities of 10,12 , and 15 years. Determine the cost to the company to fund the severance package if the bonds have (effective annual) yield rates of 10% for the 10 year bond, 11% for the 12-year bond and 12% for the 15 -year bond. Applying any of the bond price formulas from Chapter 4 gives prices of 100,000 for the 10-year bond, 93,507.64 for the 12-year bond and 86,378.27 for the 15 -year bond, for a total cost of 279,885.91. With the purchase of these bonds, the company's liabilities to the three employees are exactly matched. Best match occurs at n=15; no immunization