Question

In preparation for Thanksgiving, a Finance professor goes to Wegman’s and buys a 20-lb Fresh Young Turkey for $53.80. If the long-term average of US inflation rate is 2% per year, how much did her senior neighbor pay for a 18-lb turkey 20 years ago?

The professor hears that specialized turkey is the mainstream now. She likes the idea of giving up some quantity for better quality since she usually does not like the leftover. She is curious if her budget is the same, how small of a bird she could afford if she buys free-range turkey at $4.49/ lb (please round the number)?

She now wants to compare free-range turkey of that size with organic turkey of the same size, which is selling at $6.24/ lb and calculate how much extra would she have to pay? If that once-per-year extra spending could otherwise be put into a stock trading account that earns 8% per year, compounded quarterly, how much could have otherwise accumulated after 20 Thanksgivings if she does not go for organic turkey?

(This one requires both converting APR to EAR and a saving annuity at EAR).

Answer 1

	Current Price for 20 lb turkey	$53.80
	Long TermAverage inflation rate	2%	0.02
	Number of years in the past	20
	PV=FV/((1+i)^N)
	Fv=Future Value =$53.80
	i=Inflation rate =0.02
	N=Number of years=20
	PV=Present Value 20 years ago	$36.21	(53.80/(1.02^20)
	Amount paid 20 years ago for 20 lb turkey	$36.21
	Amount paid 20 years ago for 18 lb turkey	$32.59	(36.21/20)*18
	Price of free range turkey per lb	$4.49
	Budget available	$53.80
	Quantity of freerange turkey she can afford	11.98218	lb	(53.80/4.49)
	Cost of same size organic turkey=11.9822*6.24	$74.77
	Extra amount she needs to pay for organic turkey	$20.97	74.77-53.80
	Quarterly effective interest rate =(8/4)%	2%	0.02
	Effective Annual Interest Rate =R
	1+R=(1+0.02)^4=	1.082432
	Effective Annual Interest Rate =R=	0.082432
	Effective Annual Interest Rate =R=	8.243%
	Compount Amount Factor (CAF)=(F/A,i,N)=(((1+i)^N)-1)/i
	i=Interest Rate =8.243%=0.08243
	N=Number of years=20
	CAF=(F/A,8.243%,20)=((1.08243^20)-1)/0.08243=	47.01255
	Future Value of Savings =$20.97*CAF=	$985.80
	Amount accumulated in 20 years	$985.80