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Infinite Accountant

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Infinite Accountant

by dtweah » Thu May 14, 2009 5:31 pm
Suppose in the year 1 that $1 was invested at a rate compounded annually so that its value would double every 20 years. The value, 2000 years later, in the year 2001, would be best approximated by

(a) $1,300
(b) $1,300,000
(c) $ 1.3x1020
(d) $ 1.3x1030
(e) $1.3x1072
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Re: Infinite Accountant

by Vemuri » Thu May 14, 2009 6:30 pm
From the question we know that every 20 years the dollar value gets doubled. Also, we can derive that the doubling happens for 100 years (2000/20).

1, 2, 4, 8, 16,.......2^99

So, in 2001, the value will be 2^99.

I seem to be missing something :roll:
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Re: Infinite Accountant

by dtweah » Sat May 16, 2009 9:35 am
dtweah wrote:Suppose in the year 1 that $1 was invested at a rate compounded annually so that its value would double every 20 years. The value, 2000 years later, in the year 2001, would be best approximated by

(a) $1,300
(b) $1,300,000
(c) $ 1.3x1020
(d) $ 1.3x1030
(e) $1.3x1072
(d) Every 100 years the value is increased by multiple of 2^5. Hence by the year 2001 the value has increased by a multiple of 2^100. Since 2^10 = 1,024 > 1,000 = 10^3 it follows that 2^100 > 10^30. Since 2^10 < 2x10^3 it follows that 2^100 < (2 x 10^3)^10 < 2x10^33
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