Question

Financial Literacy1.Saving for Retirement Three brothers Frank, Gary, and Tim all plan to save for retirement. All of them plan to retire at age 65. All of them save in a retirement account that pays 4% interest. Each of them plans to save some of each paycheck and all are paid every other week (26 paychecks per year) However, each of them has a different strategy. At age 20 Frank invests $100 every two weeks. At age 30 Gary begins investing and puts $150 away every two weeks. At age 40 Tim decides to start saving and saves $200.00 every two weeks. When retirement beckons at age 65, how much will each brother have available? How much would Gary and Tim need to invest from each paycheck to match the value in Frank’s nest egg?

Answer 1

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Part-A: > The amount that Frank will have at his retirement will be $327.683.17. > The amount that Gary will have at his retirement will be $297,456.61. ► The amount that Tim will have at his retirement will be $223,105.06. Part-B: > The amount that Gary should invest in order to match Frank's nest egg is $165.24. ► The amount that Tim should invest in order to match Frank's nest egg is $293.75. Explanation: Part-A: + Frank: Using the future value of an annuity formula: FV=P((1+r)n-1)/ Where: FV is the future value (the amount Frank will have at the age of 65)= ? P is the every two week deposits= $100 ris the bi-weekly rate= 4%/26= 0.153846% or 0.00153846 n is the total number of bi-weekly periods= (65-20)*26= 45*26= 1;170 FV=P((1+r)n-1)/r FV=$100*((1+0.00153846)1170-1)/0.00153846 FV=$100*(1.001538461170-1)/0.00153846 FV=$327,683.1726 FV=$327,683.17 Therefore, the amount that Frank will have at his retirement will be $327,683.17. JI

Gary: Using the future value of an annuity formula: FV=P((1+r)n-1)/ Where: FV is the future value (the amount Gary will have at the age of 65)= ? P is the every two week deposits= $150 ris the bi-weekly rate= 4%/26= 0.153846% or 0.00153846 n is the total number of bi-weekly periods= (65-30)*26= 35*26= 910 FV=P((1+r)n-1)/r FV=$150*((1+0.00153846)910-1)/0.00153846 FV=$150*(1.00153846910-1)/0.00153846 FV=$297,456.6111 FV=$297,456.61 Therefore, the amount that Gary will have at his retirement will be $297,456.61. Tim: Using the future value of an annuity formula: FV=P((1+r)n-1)/ Where: FV is the future value (the amount Tim will have at the age of 65)= ? P is the every two week deposits= $200 r is the bi-weekly rate= 4%/26= 0.153846% or 0.00153846 n is the total number of bi-weekly periods= (65-40)*26= 25*26= 650 FV=P((1+r)n-1)/r FV=$200*((1+0.00153846)650-1)/0.00153846 FV=$200*(1.00153846650-1)/0.00153846 FV=$223,105.0628 FV=$223,105.06 Therefore, the amount that Tim will have at his retirement will be $223,105.06.

Part-B: + Gary: Using: P=FV(0)/((1+r)n-1) Where: P is the amount Gary should invest in order to match Frank's nest egg=? FV is the future value (the amount Frank will have at the age of 65)=$327,683.17 r is the bi-weekly rate= 4%/26= 0.153846% or 0.00153846 n is the total number of bi-weekly periods= (65-30)*26= 35*26= 910 P=FV(r)/((1+r)n-1) P=$327,683.17(0.00153846)/((1+0.00153846)910-1) P=$504.12745/(1.00153846910-1) P=$165.242505 P-$165.24 Therefore, the amount that Gary should invest in order to match Frank's nest egg is $165.24. + Tim: Using: P=FV(r)/((1+r)n-1) Where: P is the amount Tim should invest in order to match Frank's nest egg=? FV is the future value (the amount Frank will have at the age of 65)=$327,683.17 r is the bi-weekly rate= 4%/26= 0.153846% or 0.00153846 n is the total number of bi-weekly periods= (65-40)*26= 25*26= 650 P=FV(r)/((1+r)n-1) P=$327,683.17(0.00153846)/((1+0.00153846)650-1) P=$504.12745/(1.00153846650-1) P=$293.747857 P-$293.75 Therefore, the amount that Tim should invest in order to match Frank's nest egg is $293.75.

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