Question

Consider a person who begins contributing to a retirement plan at age 25 and contributes for 40 years until retirement at age 65. For the first 10 years, she contributes $3,000 per year. She increases the contribution rate to $5,000 per year in years 11 through 20. This is followed by increases to $10,000 per year in years 21 through 30 and to $15,000 per year for the last ten years. This money earns a 9 percent return.

First compute the value of the retirement plan when she turns age 65. (Do not round intermediate calculations and round your final answer to 2 decimal places.)

Answer 1

CASE 1

CALCULATE FOR FIRST TEN YEARS = FV =(RATE,NPER,PMT,[PV],TYPE)

RATE= 9% , NPER = 10, 3000, PV=0,TYPE=0 , SUBSTITUTING THIS IN EXCEL FORMULA,

FV=(.09,10,-3000,0,0) = $45,578.79 , THIS AMOUNT WILL ATTRACT 9% FOR REST OF 30 YEARS = FV=PV(1+R)^T , FV = VALUE AT 10TH YEAR = $45,578.79 , R = 0.09, T= 30YEARS

FV=45578.79(1.09)^30 = $604724.73

2ND CASE : AT THE AGE OF 35, FOR NEXT 10 YEARS ,CONTRIBUTES $5000,

PUTTING IN FV FORMULA, FV =(RATE,NPER,PMT,[PV],TYPE) , WE LL GET = FV(0.09,10,-5000,0,0) = 75964.65

AND FV FOR NEXT 20 YEARS = FV=PV(1+R)^T , HERE PV = 75964.65, T = 20 , R = 0.09

FV= 75964.65*(1.09)^20 = $425737.1024

3RD CASE, AT THE AGE OF 45, FOR NEXT 10 YEARS ,CONTRIBUTES $10000,

PUTTING IN FV FORMULA, FV =(RATE,NPER,PMT,[PV],TYPE),WE LL GET = FV(0.09,10,-10000,0,0) =$151929.30

AND FV FOR NEXT 10 YEARS = FV=PV(1+R)^T , HERE PV =151929.30 , T = 10 , R = 0.09

FV =151929.30*(1.09)^10 = $359671.90

4TH CASE AT THE AGE OF 55, FOR NEXT 10 YEARS ,CONTRIBUTES $15000,

PUTTING IN FV FORMULA, FV =(RATE,NPER,PMT,[PV],TYPE),WE LL GET = FV(0.09,10,-15000,0,0)

= $227893.95

SO, TOTAL VALUE AT THE AGE OF 65 = CASE1 + CASE 2 + CASE 3 + CASE 4

= $604724.73 + $425737.1024 + $359671.90+ $227893.95

FINAL VALUE AT AGE OF 65 = $1618027.68