Question 597902
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ A\ =\ P\left(1\ +\ \frac{r}{n}\right)^{nt}]


where


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


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ P] is the present value


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ r] is the annual interest rate expressed as a decimal.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ n] is the number of compounding periods in a year.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ t] is the number of years.


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


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



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


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ t\ =\ \frac{\ln\left(\frac{A}{P}\right)}{n\ln\left(\left(1\ +\ \frac{r}{n}\right)\right)}]


Plug in your given values and beat your calculator into submission.  Note:  Use of the natural logs is optional.  Choose any base you like commensurate with the capabilities of your calculator or spreadsheet.


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