Tuesday, September 30, 2008

Math Quiz

Math quiz time, stock market geniuses!

Suppose on January 1, 2009, you take $100 (Canadian) and invest it in aluminum. Now suppose that in 2009 aluminum appreciates by 11%. Then in 2010 it devalues by 10%. And it alternates like that from then on-- one year gaining 11%, the next year losing 10%, so that on average it gains 0.5% per year.

By the end of 2056, how much is your investment worth?

(a) $127.05
(b) $168.29
(c) $97.62
(d) $110.07
(e) It cannot be determined without knowing the future U.S. / Canadian exchange rate.

And a follow-up question: If someone were to offer you a fixed interest rate, instead of this up-and-down averaging 0.5%, how low an amount would you accept?

(a) 0.2%
(b) 0.3%
(c) 0.4%
(d) 0.45%
(e) 0.499%

Answers later in Comments, maybe.

8 Comments:

Blogger Johanna said...

(C) for Dec. 31, 2056. And even the 0.2% would have me coming out ahead since Jan. 1, 2056 with the roller coaster rate is $108.47, at 0.2% compound interest, $110.07. I live here, so I reserve the right to not even consider what any of this works out to in USD. I guess the strategy of retaining paper bills for tiny denominations will at least provide shelter for your freezing feet as a blankie.

9/30/08, 11:37 AM  
Blogger Scheherazade said...

This is totally implausible. Under what circumstances would aluminum ever decline in value? It's the material of the future. Buy and hold, baby. The real question is, at what age will you be when your investment lets you retire?

9/30/08, 2:59 PM  
Blogger pjm said...

No, no, no. The real question is, how much beer is contained in said aluminum? And how much would the return deposit be on 48 years worth of PBR?

9/30/08, 4:34 PM  
Blogger brushfiremedia said...

Titanium would be a better investment.

9/30/08, 7:26 PM  
Blogger Weeble said...

(c) $97.62 = (1.11*0.9)^24

(assuming this is also Canadian dollars)

(a) is the lowest I would accept of the options listed. I would take anything greater than e^(1/49*ln 1.0826)-1.

9/30/08, 8:53 PM  
Blogger Weeble said...

Whoops. $97.62 = (1.11*0.9)^24*100.

Best not do math on an empty stomach...

9/30/08, 8:55 PM  
Anonymous Anonymous said...

You're all approaching this from the wrong perspective. Around here, no one "invests" in aluminum (or copper or other metal) because they can make a quicker profit stripping vacant houses and selling it for scrap.

By 2056, the money will all have been spent, which will be moot, because the "investors" will all have died in prison.

None of you are in forensics, are you?

10/1/08, 9:09 AM  
Anonymous Pop said...

$97.62 and (a), but all in US Dollars.
This reminds me of one of my favorites:
A store will give you two discounts - 5% off for being a senior citizen and 3 % off because it is Wednesday. What is the best order to apply these discounts?

10/4/08, 5:11 PM  

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