Question

Discounted Cash Flow Valuation

You and your spouse begin immediately saving for retirement and the dreamy “ever after” that you need to fund. At this point, your “ever after” fund has a balance of $0. You begin depositing $300 each month, starting one month from now, for the next 30 years. Your spouse begins depositing $5,000 each year, starting one year from now, into the same account for the next 30 years. The joint account earns 9 percent APR, compounded monthly. How much will you two have in your joint account 30 years from now, immediately after your last deposits?

Part B Your “ever after” is expected to be funded by monthly withdrawals, starting one month after your last deposits, and it is expected to last for 35 years. How much will you two (collectively) have to happily spend each month, assuming your accounts continue to earn the same rate as before?

Answer 1

part A
1)
Future value of annuity				=	Amt[{(1+r)^n}-1]/r
	Future value of annuity of $300 per month by YOU
			Where
			amount	=	$300
			rate (.r)	=	9%/ 12 months a year=0.75% or 0.0075
			time=t	=	30yrs*12 months a year = 360
	Future value of annuity (after 30 years)			=	$300*[{(1+0.0075)^360}-1]/0.0075
				=	$300*[{(1.0075)^360}-1]/0.0075
				=	$300*[14.7306-1]/0.0075
				=	$300*[13.7306]/0.0075
				=	$300*1830.7435
				=	$549,223.05
	Future value of annuity of $5000 per year by YOUR SPOUSE
			Where
			amount	=	$5,000
	Effective annualrate (.r)			=	[(1+APR/12)^12]-1
				=	[{1+(0.09/12)}]^12]-1
				=	[(1+0.0075)^12]-1
				=		1.093807-1
				=		0.093807 or 9.3807%
				=
			time=t	=	30yrs*12 months a year = 360
	Future value after 30 years			=	$5000[{(1+0.093807)^30}-1]/0.093807
				=	$5000[14.7306-1]/0.093807
				=	$5000*[13.7306]/0.093807
				=	$5000*146.3709
				=	$    731,854.50
Total amount in 'ever after" after 30 years				=	Future value of your annuity+future value of your spouse annuity
				=	$549,223.05+$731,854.5
				=	$1,281,077.55
Part B
annual payment per month next 35years(Present value of annuity)
				=	Amt[1-(1+r)^-n]/r
			here
	Present value of annuity			=	$1,281,077.55
			r	=	9%/12 months a year=0.75% or 0.0075
			time=n=		35 years*12 months a year=420
			amt	=	?
			$1,281,077.55	=	Amt[1-{(1+0.0075)^-420}]/0.0075
			$1,281,077.55	=	Amt[1-{(1-0.043359]/0.0075
			$1,281,077.55	=	Amt[0.955664/0.0075]
			$1,281,077.55	=	Amt*127.5521
		$1,281,077.55/127.5521		=	Amt
			$      10,043.56	=	Amt
	Monthly spends =$10,043.56
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