Question

You make an initial investment of $5,000 in an account that pays 6.75% interest compounded
semi-annually.

How long will it take for the account to have $7,500 in it?

Answer 1

http://openstudy.com/updates/538510e6e4b07cf9dcd34620 <--- same way, same formula

Answer 2

but how do you do that?

Answer 3

same way as show on the other one
you'd use the same "compound interest" formula

Answer 4

just keep in mind the cycle period -> compounded semi-annually.

Answer 5

A + P (1 + r/n)^rt ?

Answer 6

hmmm actually.... I see the issue... you have to solve for "t" or years.... ok

have you covered logarithms yet?

Answer 7

kind of, I'm still a little confused with it

Answer 8

\(\bf A=P\left(1+\frac{r}{n}\right)^{nt}\implies
\cfrac{A}{P}=\left(1+\frac{r}{n}\right)^{nt}
\\ \quad \\
\textit{log cancellation rule of }log_{\color{red}{ a}}({\color{red}{ a}}^x)=x\qquad thus
\\ \quad \\
\large log_{\left(1+\frac{r}{n}\right)}\frac{A}{P}=
log_{\left({\color{brown}{ 1+\frac{r}{n}}}\right)}\left[{\color{brown}{ 1+\frac{r}{n}}}\right]^{nt}\implies
log_{\left(1+\frac{r}{n}\right)}\frac{A}{P}=nt
\\ \quad \\
\large \cfrac{log_{\left(1+\frac{r}{n}\right)}\frac{A}{P}}{n}=t\)

Answer 9

well \(\bf A=P\left(1+\frac{r}{n}\right)^{nt}\implies
\cfrac{A}{P}=\left(1+\frac{r}{n}\right)^{nt}
\\ \quad \\
\textit{log cancellation rule of }log_{\color{red}{ a}}({\color{red}{ a}}^x)=x\qquad thus
\\ \quad \\
\large log_{\left(1+\frac{r}{n}\right)}\left[\frac{A}{P}\right]=
log_{\left({\color{brown}{ 1+\frac{r}{n}}}\right)}\left[{\color{brown}{ 1+\frac{r}{n}}}\right]^{nt}\implies
log_{\left(1+\frac{r}{n}\right)}\left[\frac{A}{P}\right]=nt
\\ \quad \\
\large \cfrac{log_{\left(1+\frac{r}{n}\right)}\left[\frac{A}{P}\right]}{n}=t\)