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# Derek plans to retire on his 65th birthday. However, he plans to work part-time until he...

Derek plans to retire on his 65th birthday. However, he plans to work part-time until he turns 72.00. During these years of part-time work, he will neither make deposits to nor take withdrawals from his retirement account. Exactly one year after the day he turns 72.0 when he fully retires, he will wants to have \$2,823,229.00 in his retirement account. He he will make contributions to his retirement account from his 26th birthday to his 65th birthday. To reach his goal, what must the contributions be? Assume a 9.00% interest rate.

 Future value = present value*(1+ rate)^time 2823229 = Present value*(1+0.09)^7 Present value = 1544402.94 Using Calculator: press buttons "2ND"+"FV" then assign FV =-2823229 I/Y =9 N =7 PMT = 0 CPT PV Using Excel =PV(rate,nper,pmt,FV,type) =PV(0.09,7,,2823229,)
 FVOrdinary Annuity = C*(((1 + i/100)^n -1)/(i/100)) C = Cash flow per period i = interest rate n = number of payments 1544402.94= Cash Flow*(((1+ 9/100)^40-1)/(9/100)) Cash Flow = 4570.83 Using Calculator: press buttons "2ND"+"FV" then assign FV =1544402.94 I/Y =9 N =40 PV = 0 CPT PMT Using Excel =PMT(rate,nper,pv,fv,type) =PMT(9/(100),40,,1544402.94,)

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