Question 359737
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The formula for the future value of an investment at discretely compounded interest is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ A\ =\ P\left(1\ +\ \frac{r}{m}\right)^{mt}]


where


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ A] represents the future value


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ P] represents the initial investment


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ r] is the interest rate as a decimal (*[tex \Large \frac{r%}{100}])


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ m] is the number of compounding periods per interest term (per year for annual interest rate)


and


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ t] is the number of terms (years for annual interest rate)


You don't know *[tex \Large A] or *[tex \Large P], but you do know that *[tex \Large \frac{A}{P}\ =\ 4] and that we can write the original formula as:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{A}{P}\ =\ \left(1\ +\ \frac{r}{m}\right)^{mt}]


Next, fill in the values you know and simplify:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(1\ +\ \frac{.2}{1}\right)^{t}\ =\ 4]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(1.2\right)^{t}\ =\ 4]


Take the log of both sides (base 10 or natural, doesn't matter which)


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ln\left(1.2\right)^{t}\ =\ \ln(4)]


Use the laws of logs:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ t\ln\left(1.2\right)\ =\ \ln(4)]


Divide by *[tex \Large \ln\left(1.2\right)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ t\ =\ \frac{\ln(4)}{\ln(1.2)}]


The rest is arithmetic on the calculator.


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