[tex]\begin{gathered} \text{ The formula for compound interest is} \\ A=P(1+\frac{r}{n})^{nt} \\ \text{ Rearranging the formula so that we solve for time and we get} \\ t=\frac{\ln (\frac{A}{P})}{n\lbrack\ln (1+\frac{r}{n})\rbrack} \\ \text{The given that we have are} \\ P=5000 \\ A=5925 \\ r=0.03\text{ this is derived from 3\% converted to decimal} \\ n=12\text{ Since this is compounded monthly} \\ \text{Substitute the following values and we have} \\ t=\frac{\ln(\frac{A}{P})}{n\lbrack\ln(1+\frac{r}{n})]} \\ t=\frac{\ln (\frac{5925}{5000})}{12\lbrack\ln (1+\frac{0.03}{12})\rbrack}\text{ Input this in a scientific calculator and we get} \\ t=5.67\text{ years, rounded off to the nearest hundredth} \end{gathered}[/tex]
