$1.$ John Wilson is a $42$ year$-$old computer programmer, husband and father of four. He wants to use the capital retention approach to determine how much life insurance he should purchase. Because of his $$105,000$ salary and their four children, his wife does not work outside the home. The family$$s current annual living expenses are approximately $$75,000,$ including $$8,000$ in annual IRA contributions. He prefers to use the capital retention approach so that he can be reasonably assured that his family will not exhaust the proceeds of his policy; however, he also wants to consider the possible reduction in expenses and apply a $70\%$ replacement ratio to the calculation.

a$.$ Calculate John$$s insurance need using the capital retention approach, an after$-$tax discount rate of $5\mathrm{.}5\%,$ and assume end$-$of period payment of benefits. Show your work.

b$.$ Calculate John$$s insurance need using the human life value approach, an after$-$tax discount rate of $5\mathrm{.}5\%,$ a remaining working life of $25$ years, and assume end$-$of period payment of benefits. Show your work.