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# Compound Interest.

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At what interest rate, compounded annually, would 1/1,000,000 of 1 cent be worth 1 penny in 1,000 years from now?  Serious question given by our Math teacher to see if we understand compound interest! Thanks for help.

Nov 7, 2018

### 2+0 Answers

#1
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FV = PV (1+i)^n

1 = 1x10^-6 (1+i)^1000

1/1x10^-6 = (1+i)^1000

10^6 = (1+i)^1000                  take log of both sides

6 = 1000 log(1+i)

6/1000 = log (1+i)       raise 10 to both sides

10^(6/1000) = 1+i

i=1.3911%

Nov 7, 2018
#2
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Here is another way!

1 =1/1,000,000 x (1 +i)^1,000      divide both sides by 1/1,000,000

1,000,000 = (1 +i)^1,000               take 1/1,000th root of both sides

1,000,000^(1/1,000) = 1 + i

1.013911385........     = 1 + i           subtract 1 from both sides and multiply by 100

i =1.3911385%.

Nov 7, 2018