SOLUTION: Kate wants her $9000 GIC to double in value in nine years. What annual rate of interest is required for her to reach her goal. Assume interest is compounded annually. Can this be

Question 128055: Kate wants her $9000 GIC to double in value in nine years. What annual rate of interest is required for her to reach her goal. Assume interest is compounded annually.
Can this be done without using natural logs and just using "logs" OR are both of these the same thing ?????????????
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
natural logs (base e) are used for continuous compounding __ A=Pe^(rt)

the compound interest calculation is exponential, so depending on what quantity you're trying to find,
__ logs are involved

the only difference between "logs" (common logarithms) and natural logs is the base
__ common logs are base 10, natural logs are base e (Euler's number)

A=P(1+r)^n where A=amount; P=principle (starting amount);
__ r=interest rate per compounding period; n=number of compounding periods

18000=9000(1+r)^9

dividing by 9000 __ 2=(1+r)^9

taking log __ log(2)=9(log(1+r))

dividing by 9 __ (log(2))/9=log(1+r)

taking antilog __ 10^(log(2)/9)=1+r __ 10^(log(2)/9)-1=r
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