Question

Today is your 25th birthday (Happy Bday!). You plan on retiring 35 years from today. Every month you work, starting today (t=0), 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?

Answer 1

	We would calculate the present value of withdrawal required for 20 years of $ 10000
	By Using PV function we get
	PMT	$10,000
	NPER	240	20*12
	Rate	0.75	9%/12
	($1,111,449.54)		PV(0.75%,240,10000)
	Present Value on 60th Birthday - $ 1111449.54
	Present Value of $ 100000 at 20th year
	Interest Rate = (1.0075^12) - 1
		9.38%
	Present Value of 100000 is 100000*(1/1.0938^20)
	Present Value on 60th year = $ 16641.28
	Present Value of Total withdrawal on 60th Birthday = (1111449.54+16641.28)							1128090.82
	Using the PMT function we get monthly payment as
	($383.47)				PMT(0.75%,(35*12),,1128090.82)
	Amount to be deposit is $ 383.47 per month