The compound interest formula is:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where A is the final amount, P is the principal, r is the annual interest rate (as a decimal), n is the number of times interest is compounded per year, and t is time in years.
Substituting with P = $41.67, r = 0.045 (=4.5/100), n = 365 (the interest is compounded daily), and t = 3 years, we get:
[tex]\begin{gathered} A=41.67(1+\frac{0.045}{365})^{365\cdot3} \\ A=41.67(1.00012)^{1095} \\ A=47.69\text{ \$} \end{gathered}[/tex]