Question 196039: Solve this application using logarithms.
At what interest rate compounded annually will money in savings double in five years?
I do not understand how to do the or what the logarithms mean in this problem. Thanks for your help
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! Start with the compound interest formula
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A = P (1+r) ^t,,,where A is Total, P is starting Principal,,,r is rate, t is time (yrs)
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But to double means A =2P
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2P = P(1+r)^t
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divide by P thruout
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2 = (1+r)^t
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Take log both sides
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log2 = log (1+r)^t = t log(1+r),,,, from log x^2=2logx
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But,,,t=5,,,given
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log2 =5log(1+r)
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log2 /5 = .0602 = log(1+r)
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Raise both sides to power of 10,,that is 10^.0602 =10^ (log (1+r))
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1.148 = (1+r),,,remember 10^(log x) =x
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(.148) =r,,,,,answer,,,or 14.8 %
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checking
A/P = (1 +r)^5 = (1.148)^5 = 2,,,,ok
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