HOw many years will it take an investment of $35,000 to grow to$50,000 it it is invested at 4.75% compounded continuously
The answer is 7.51yr
Answers
Answered by
3
P = $35,000
A = $50,000
r = 4.75%
time, t = ?
![A=P[1+ \frac{r}{100} ]^t\\ \\ \Rightarrow 50000=35000[1+ \frac{4.75}{100} ]^t\\ \\ \Rightarrow \frac{50000}{35000} =[1+ 0.0475} ]^t\\ \\ \Rightarrow \frac{10}{7} =[1.0475 ]^t\\ \\take\ log\ on\ both\ sides\\ \\ \Rightarrow log( \frac{10}{7}) =log([1.0475 ]^t)=t\ log(1.0475)\\ \\ \Rightarrow t= \frac{log( \frac{10}{7} )}{log(1.0475)} \\ \\ \Rightarrow t = 7.68\ years](https://tex.z-dn.net/?f=A%3DP%5B1%2B+%5Cfrac%7Br%7D%7B100%7D+%5D%5Et%5C%5C+%5C%5C+%5CRightarrow+50000%3D35000%5B1%2B+%5Cfrac%7B4.75%7D%7B100%7D+%5D%5Et%5C%5C+%5C%5C+%5CRightarrow++%5Cfrac%7B50000%7D%7B35000%7D+%3D%5B1%2B+0.0475%7D+%5D%5Et%5C%5C+%5C%5C+%5CRightarrow++%5Cfrac%7B10%7D%7B7%7D+%3D%5B1.0475+%5D%5Et%5C%5C+%5C%5Ctake%5C+log%5C+on%5C+both%5C+sides%5C%5C+%5C%5C+%5CRightarrow+log%28+%5Cfrac%7B10%7D%7B7%7D%29+%3Dlog%28%5B1.0475+%5D%5Et%29%3Dt%5C+log%281.0475%29%5C%5C+%5C%5C+%5CRightarrow+t%3D+%5Cfrac%7Blog%28+%5Cfrac%7B10%7D%7B7%7D+%29%7D%7Blog%281.0475%29%7D+%5C%5C+%5C%5C+%5CRightarrow+t+%3D+7.68%5C+years "A=P[1+ \frac{r}{100} ]^t\\ \\ \Rightarrow 50000=35000[1+ \frac{4.75}{100} ]^t\\ \\ \Rightarrow \frac{50000}{35000} =[1+ 0.0475} ]^t\\ \\ \Rightarrow \frac{10}{7} =[1.0475 ]^t\\ \\take\ log\ on\ both\ sides\\ \\ \Rightarrow log( \frac{10}{7}) =log([1.0475 ]^t)=t\ log(1.0475)\\ \\ \Rightarrow t= \frac{log( \frac{10}{7} )}{log(1.0475)} \\ \\ \Rightarrow t = 7.68\ years")
A = $50,000
r = 4.75%
time, t = ?
Similar questions