Retirement Planning InfoAn individual is currently 30 years old and sh

QUESTION

Retirement Planning InfoAn individual is currently 30 years old and she is planning her financial needs upon retirement. She will retire at age 65 (exactly 35 years from now) and she plans on funding 20 years of retirement with her investments. Ignore any social security payments and ignore any taxe
This question has 3 parts :- 1. First FInd the Amount PMTr needed per year from Age 65 to 85 ie 20 yrs. Today she is 30 Yr old. First withdrawl is 75% of $71,000 = $53,250=PMTr. This withrwal will happen for Nr=20yrs. DUring this period, her lump sum will reduce & will earn Interest Ir=7.5%. So here we have to find the PV of ANnuity Due of PMT = $53250 for Ir=7.5% & Nr=20. It is Annuity due as first payment happens immediately when she turns 65 & not a year later. 2. Present Return rate is 11%, Inflation is 1%. SO Net Rate of Return i = 11%-1% =10%. 3. SO at AGe 65, she will have a Lump sum which is arrived at at ‘1 above which is Future Value of Annuity. This annuity has PMT every year for N1=35Yrs at i=10% to get the Retrtment Kitty. So we need to find PMT here So lets start :- A) How much money will she need to withdraw each year starting at age 65 to have the same purchasing power as today? Ans : 71000*75% = $53250(ANS 1) B) How much money must she have at age 65 in order to make her planned withdrawals? See note 1 above.

Present value of annuity due PVA = PMT(PVIFAi,n)*(1 i) So PVA = PMTr*(1/Ir 1/(Ir(1 Ir)^Nr))*(1 Ir) So we get PVA = 53250*(1/7.5% -1/(7.5%*(1 7.5%)^20)) *(1 7.5%) ie PVA =53250*10.1945*1.075 So PVA = $ 583,571.41 So at Age 65yrs, She should have $ 583,571.41 ..(ANS 2) C) How much should she save per year starting right now in order to have the retirement annuity she desires? See note 3 above We have to Find Fv of Annuity. FVAn= PMT(FVIFAi,n) Here we have FVA = 583,571.41 , N1=35, i=10% So we have FVAn = PMT*[(1 i)^n-1]/i Putting values we get 583,571.41 = PMT*((1 10%)^35 1)/10% = PMT*( 27.1024)/10% = 271.024*PMT ie PMT = $583,571.41 /271.024 = $ 2,153.21 So She should save $2,153.21 per year.

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