The compound interes formula is given by:
[tex]P_N=P_0(1+\frac{r}{k})^{Nk}[/tex]where P0 is the principal (the initial amount), r is the interes rate (in decimal form), k is the number of times the interest is compounded and N is the time elapsed.
Plugging the values given we have:
[tex]\begin{gathered} P_N=10000(1+\frac{0.04}{12})^{12\cdot25} \\ =27,137.65 \end{gathered}[/tex]Therefore the future amount is $27,137.65 and the interest earned is $17,137.65.
