Question

2. You will receive $5,000 one year from now, 6000 three years from now, and 7000 five years from now in real terms. Each payment will be received at the end of the period with the first payment occurring one year from today. The relevant nominal discount rate is 9.625 percent and the inflation rate is 2.3 percent. What are your winnings worth today in real dollars?

Answer 1

2)	Nominal rate	=	9.625% or 0.09625
	Inflation rate	=	2.3%or 0.023
	Real Rate	=	[(1+nominal rate) / (1+inflation rate)]-1
		=	[(1+0.09625) / (1+0.023)]-1
		=	[1.09625/1.023]-1
		=	1.07160-1
		=	0.0716	or 7.16%
	Value today	=	Sum of (payment in year * PVAF of respective year)
		=	[$5,000*PVAF(7.16%,1)]+[$6,000*PVAF(7.16%,3)]+[$7,000*PVAF(7.16%,5)]
		=	[$5,000*0.9332]+[$6,000*0.8126]+[$7,000*0.7077]
		=	$4665.92+$4875.88+$4953.76
		=	$ 14,495.56
3)	Price of bond		=	PV of all interest payment+PV of redemption value
			=	[Coupon * PVAF (YTM,years to maturity)]+[PVF(YTM,years) *redemption value]
	When Bond was purchased In 2009
	Coupon(semi annual)		=	$1000*7.5%*6/12=$37.5
	Years (bond issued in 2001)		=	25 years - 8years = 17 years or 34 half years
		YTM	=	7.8%*6/12=3.9% per half year
		Redemption value	=	$1,000
		Price	=	[$37.5*PVAF(3.9%,34)]+[PVF(3.9%,34)*$1000]
			=	[$37.5*18.6586]+[$1,000*0.2723)
			=	$699.7+$272.31
			=	$ 972.01
	When Bond was sold In 2013
	Coupon(semi annual)		=	$1000*7.5%*6/12=$37.5
		Years	=	25 years - 12 years = 13 years or 26 half years
		YTM	=	10.6%*6/12=5.3% per half year
		Redemption value	=	$1,000
		Price	=	[$37.5*PVAF(5.3%,26)]+[PVF(5.3%,26)*$1000]
			=	[$37.5*13.9409]+[$1,000*0.2611)
			=	$522.78+$261.13
			=	$ 783.91
	Percentage change in price		=	[(sale price-purchase price)/Purchase price]*100
			=	[( $783.91-$972.01)/$972.01]*100
			=	( - $188.1/$972.01)*100
			=	- 0.192517 or -19.2517%
	There may be little difference due to decimal places,please do not downvote on that basis
	If you have any doubt,please ask
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