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Question 455271: I need help with this problem:
Specify the range of f(x)=x -[x], where [x] is the greatest-interger function. Use the compound interest formula to prove the rule of 70: investment doubling time 70 where r is the nominal interest rate expressed as a percentage (number between zero and 100).
Thank you!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! I need help with this problem:
Specify the range of f(x)=x -[x], where [x] is the greatest-integer function.
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Graph y = x
Graph y = [[x]]
Range = [0,1)
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Use the compound interest formula to prove the rule of 70: investment doubling time 70 where r is the nominal interest rate expressed as a percentage (number between zero and 100).
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Let P be the pricipal.
Doubling 2P = Pe^(rt)
e^(rt) = 2
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Take the natural log to get
rt = ln2
t = (0.69)/r
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time = 69/(interest rate expressed as a whole number)
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Example:
at 8% doubling time = 69/8 = 8.65 years
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Cheers,
Stan H.
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