Today is your 25th birthday (Happy Bday!). You plan on retiring 35 years from to

Question

Today is your 25th birthday (Happy Bday!). You plan on retiring 35 years from today. Every month you work, starting today, you wish to put an equal amount of money into a savings account with your last deposit on the day you retire. After you retire, you will need to withdraw 10,000 a month with your last withdrawal on your 80th birthday (first withdrawal is one month after you retire). Also when you turn 80, you plan on giving $100,000 to your grandchildren.

If the annual rate of interest is 9% (compounded monthly), how much do you need to deposit each month into your savings account?

NOTE: ROUND ANSWER TO THE NEAREST 10. If answer equals $1,356.32, enter 1360 as your answer.

Explanation / Answer

We have Int Rate = Rate = 9% monhly = 9%/12 We have period of deposit = 35 Yrs. As deposit ismonthly, we have nper = 35Yr*12 mon/Yr = 420 periods We ahave from Age of 25+35 = 60 to 80, period is 20 Yrs = 20*12 = 240 months You withdraw 10000 per month. SO PMT = 10,000 At end of 20 Yrs ie age 80, you have $100,000 balance for your grandson. So Your Corpus at Age 60 = PV(Rate,nper,PMT,FV) = PV(9%/12,240,10000,100000) ie Corpus at Age 60 = $1,128,091 To get $1,128,091 at Age 60, we need to make monthly payment which are found as below. Monthly Pmt = PMT(Rate,nper,PV,FV) = PMT(9%/12,420,0,1128091) = $383 So you need to deposit $383 each month into your savings account

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