Question 310820
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To turn 1000 into 1000000, you need to multiply by 1000.  Assuming that the interest only compounds annually:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 1000(1.06)^n\ =\ 1000000]


and solve for *[tex \Large n]


Divide both sides by 1000


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (1.06)^n\ =\ 1000]


Take the base 10 log of both sides:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \log(1.06)^n\ =\ \log(1000)]


Then since *[tex \Large \log(1000)\ =\ 3],


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ n\log(1.06)\ =\ 3]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ n\ =\ \frac{3}{\log(1.06)}\ \approx\ 118.5] years


The boy needs to increase his initial investment a bit, n'est-ce pas?


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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