Suppose you would like to be able to withdraw $240,000 per year for 30 years you...

Suppose you would like to be able to withdraw $240,000 per year for 30 years you are retired. How much do you need to save for the 45 years you are working reach this goal? Assume that you can earn 5% on your investments during your retirement and 7.5% in the years you are saving. Also, assume begin saving in year 1 and don’t make your first withdraw until year 46.

Expert Solution


Step 1:	Present value of annual withdrawal for 30 yearsi.e. amount should be available at the end of year 45
	Present Value Of An Annuity
	= C*[1-(1+i)^-n]/i]

	Where,
	C= Cash Flow per period
	i = interest rate per period
	n=number of period

	= $240000[ 1-(1+0.05)^-30 /0.05]

	= $240000[ 1-(1.05)^-30 /0.05]

	= $240000[ (0.7686) ] /0.05

	= $3,689,388.25

Step 2:	Calculation of annual saving
	Future Value of an Ordinary Annuity
	= C*[(1+i)^n-1]/i

	Where,
	C= Cash Flow per period
	i = interest rate per period
	n=number of period

	$3689388.25= C[ (1+0.075)^45 -1] /0.075

	$3689388.25= C[ (1.075)^45 -1] /0.075

	$3689388.25= C[ (25.9048 -1] /0.075]

	C =11110.46


	Annual Saving Should be = $11,110.46

jeff jeffy answered 1 year ago

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