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 October 31st, 2013, 05:45 PM #1 Newbie   Joined: Oct 2013 Posts: 6 Thanks: 0 Economics based on investment Hi I am in dia need of help on the following question can someone please help. A retired junk yard operator, Edsel Studebaker, recently died and left his entire fortune of $12,300,000toatrusttoestablishajunkcarmuseum. Thetrusteesmustdecidehowtospendit. Landcanbepurchasedfor$180,000now. Themuseumbuildingwillrequire30,000squarefeet of administrative and work space. Each car displayed will require an additional 1000 square feet. Planning will cost $100,000 immediately. Building construction will cost$100 per square foot and will take the next two years (assume equal costs each year.) Cars will cost $500 each (they're junk, remember?) and they will be purchased during the second year of construction. Annual operation ofthe museum will cost$200,000 plus $30 per car. Ifthe funds are invested at 9% per year and the museum is to exist forever, how many cars should the trustees plan to purchase? Any help would be great, cheers.  October 31st, 2013, 06:02 PM #2 Newbie Joined: Oct 2013 Posts: 6 Thanks: 0 Re: Economics based on investment Sorry the sentence above I've left out a series of spaces. Here is the question again for easier reading. A retired junk yard operator, Edsel Studebaker, recently died and left his entire fortune of$12,300,000 to a trust to establish a junk car museum. The trustees must decide how to spend it. Land can be purchased for $180,000 now. The museum building will require 30,000 square feet of administrative and work space. Each car displayed will require an additional 1000 square feet. Planning will cost$100,000 immediately. Building construction will cost $100 per square foot and will take the next two years (assume equal costs each year.) Cars will cost$500 each (they're junk, remember?) and they will be purchased during the second year of construction. Annual operation ofthe museum will cost $200,000 plus$30 per car. Ifthe funds are invested at 9% per year and the museum is to exist forever, how many cars should the trustees plan to purchase?
 October 31st, 2013, 09:25 PM #3 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 Re: Economics based on investment Code: YR TRANSACTIONS INTEREST BALANCE 0 12,300,000[1] -280,000[2] 12,020,000 1 -1,500,000[3] 1,081,800 11,601,800 2 -1,500,000[3] -100,500C[4] 1,044,162 11,145,962 - 100,500C 3 -200,000[5] -30C[6] ? ? Solve for C: .09(11145962 - 100500C) = 200000 + 30C C = 88.499... so 88 cars 0 12,300,000 -280,000 12,020,000 1 -1,500,000 1,081,800 11,601,800 2 -1,500,000 -8,844,000 1,044,162 2,301,962 3 -200,000 -2,640 207,178 2,306,500 4 -200,000 -2,640 207,585 2,311,445 C = number of Cars. [1] from estate [2] right away expenses: 180,000 + 100,000 [3] admin sq. footage: 30,000 @ $100 = 3,000,000: 1,500,000 year1 and year2 [4] per car purchase: 1,000 sq.ft @$100 = 100,000 + 500 = 100,500 [5] annual operating expenses, beginning year3 [6] per car annual expense, beginning year3 Note that fund increases slightly: due to 88 cars instead of 88.49... Enough for a huge xmas party each year :P
 November 3rd, 2013, 04:47 PM #4 Newbie   Joined: Oct 2013 Posts: 6 Thanks: 0 Re: Economics based on investment Thank you so much Denis this is great!! Just one question, to solve for c how did you rearrange the equation to do so? Cheers.
November 3rd, 2013, 06:42 PM   #5
Math Team

Joined: Oct 2011

Posts: 14,597
Thanks: 1038

Re: Economics based on investment

Quote:
 Originally Posted by Kaiso Just one question, to solve for c how did you rearrange the equation to do so?
Huh? You mean your teacher gives you this involved problem,
but has not teached how to solve such a basic equation?
Or did you skip classes in order to go to the poolroom? :P

Ok; the equation looks like this:
5(10 - 2c) = 4 + 3c
Multiply what's inside brackets by 5:
50 - 10c = 4 + 3c ; continue...
13c = 46
c = 46/13

OK?

 November 3rd, 2013, 07:01 PM #6 Newbie   Joined: Oct 2013 Posts: 6 Thanks: 0 Re: Economics based on investment Hahahaha Algebra always confused me with the chopping and changing either side of the =, Thank you heaps for your feed back, I appreciate it.

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