How to the missing value?

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Answer 1 · 2017-10-14T20:42:15

$\frac{log (2)}{log (1.087)} \approx 8.309$ $log(2)/log(1.087)~~8.309$ years

Initial Investment = $\frac{19000}{2} = 9500$ $19000/2=9500$

let $y$ $y$ be the number of years it will take to double

$9500 \cdot {1.087}^{y} = 19000$ $9500 * 1.087^y=19000$

$\Rightarrow {1.087}^{y} = 2$ $=>1.087^y=2$

logarithmic rules state $log (a^{x}) = x \cdot log (a)$ $log(a^x)=x*log(a)$

$\Rightarrow log ({1.087}^{y}) = log (19000)$ $=>log(1.087^y)=log(19000)$

$\Rightarrow y \cdot log (1.087) = log (19000)$ $=>y*log(1.087)=log(19000)$

$\Rightarrow x = \frac{log (2)}{log (1.087)} \approx 8.309$ $=>x=log(2)/log(1.087)~~8.309$ years