SOLUTION
We will use the formula
[tex]\begin{gathered} A=P(1+r)^t \\ A=9,000 \\ P=4700 \\ r=4.5\%=\frac{4.5}{100}=0.045 \\ t=? \end{gathered}[/tex]Applying we have
[tex]\begin{gathered} 9,000=4700(1+0.045)^t \\ 9,000=4,700(1.045)^t \\ (1.045)^t=\frac{9,000}{4,700} \\ (1.045)^t=1.91489361 \\ \end{gathered}[/tex]Taking log we have
[tex]\begin{gathered} log(1.045)^t=log(1.9148361) \\ tlog(1.045)=log(1.9148361) \\ t=\frac{log(1.9148361)}{log(1.045)} \\ t=14.75938 \end{gathered}[/tex]Hence the time is approximately 15 years
