Question

Timber Inc. invested profits of $150,000.00 in a GIC at 4.90% compounded quarterly. How long will it take for the investment to grow to a value of at least $223,000.00?____years ____months

Answer 1

The invested profit is: 150000

Formula of compund interest is:

$P=\frac{A}{(1+\frac{r}{n})^{nt}}$

Where,

P= principal amount

A= value of investment.

r=rate

n= number of times interest is compount per unit time

t= time

$\begin{gathered} P=\frac{A}{(1+\frac{r}{n})^{nt}} \\ 150000=\frac{223000}{(1+\frac{4.9}{\frac{1}{4}})^{\frac{1}{4}t}} \\ (1+4.9\times4)^{\frac{1}{4}t}=\frac{223000}{150000} \\ 20.6^{4t}=1.4866 \end{gathered}$

$\begin{gathered} 4t\ln 20.6=\ln 1.4866 \\ 4t=\frac{\ln 1.4866}{\ln 20.6} \\ t=0.032 \end{gathered}$