Question 1026215
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The amount of the original investment is immaterial.  For a given annual interest rate and compounding frequency, it takes just as long for 10 cents to triple as it does $10K. That's because, in order for the investment to triple, *[tex \Large \frac{A}{P}\ =\ 3]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ A\ =\ P(1\ +\ i)^n]


7% per annum is 1.75% per quarterly compounding period, so


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (1.0175)^n\ =\ 3]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \log(1.0175)^n\ =\ \log(3)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ n\log(1.0175)\ =\ \log(3)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ n\ =\ \frac{\log(3)}{\log(1.0175)}]


The rest is just calculator work.  Remember, *[tex \Large n] is the number of compounding periods it takes for the investment to triple, so divide by 4 to get the number of years.  Round up.


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

*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  

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