Question 609183
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ A\ =\ P\left(1\ +\ \frac{r}{n}\right)^{nt}]


And you want *[tex \LARGE \frac{A}{P}\ =\ 3], hence


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(1\ +\ \frac{r}{n}\right)^{nt}\ =\ 3]


where *[tex \LARGE r\ = 0.05] and *[tex \LARGE n\ =\ 365]


take the log (base doesn't matter) of both sides:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \log\left(1\ +\ \frac{r}{n}\right)^{nt}\ =\ \log(3)]


Use the laws of logs


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ nt\log\left(1\ +\ \frac{r}{n}\right)\ =\ \log(3)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ t =\ \frac{\log(3)}{n\log\left(1\ +\ \frac{r}{n}\right)}]


Just plug in your given values and do the arithmetic on your calculator.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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