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problemset_2005-6_key4714

problemset_2005-6_key4714 - Problem Set 6 EMA 4714...

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Problem Set 6 EMA 4714 - Materials Selection and Failure Analysis KEY Due Monday, April 4, 2005 - 11:45 am Dieter Exercise 13.4 A father desires to establish a fund for his new child’s college education. He estimates that the current cost of a year of college education is $12,000 and that the cost will escalate at an annual rate of 4 percent. [a] What amount is needed on the child’s eighteenth, nineteenth, twentieth and twenty-first birthdays to provide for a 4-year college education? *********************************************************************** F = P[F/P,i,n] = 12k/[P/F,4,17] = 12k/0.51337 = $23,400 on 18th birthday = 23.4[1.04] 1 = $24,300 on 19th birthday = 23.4[1.04] 2 = $25,300 on 20th birthday = 23.4[1.04] 3 = $26,300 on 21st birthday [b] If a rich aunt gives $5000 on the day the child is born, how much must be set aside at 10 percent on each of the first through seventeenth birthdays to build up the college fund? *********************************************************************** Converting the amounts required on 19th, 20th and 21st birthdays to a present worth on the 18th birthday [i = 10%]: P(17) = 23.4k+24.3k[P/F,10,1]+25.3k[P/F,10,2]+26.3k[P/F,10,3] P(17) = 23.4k+24.3[0.90909]+25.3k[0.82645]+26.3k[0.75131] P(17) = $86,200 as far as the $5k gift, F(17) = 5k[F/P,i,n] = 5k/[P/F,10,17] = 5k/0.19784 F(17) = $25,300 A = [P(17)-F(17)][A/F,i,n] = 61k/[F/A,10,17] = 61k/40.54470
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