Given:
Amount of money A to which a principal investment P will grow after t years at interest rate r, compounded n times per year, is given by the formula,
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]a) P= $4000, r=3% compounded daily.
The function A that models the amount to which the account grows after t years is,
[tex]\begin{gathered} A=4000(1+\frac{3}{100(365)})^{365t} \\ A=4000(1+\frac{0.03}{365})^{365t} \end{gathered}[/tex]b) after 30 years the amount will be,
[tex]\begin{gathered} A=4000(1+\frac{0.03}{365})^{365t} \\ A=4000(1+\frac{0.03}{365})^{365(30)} \\ A=4000(1.00008)^{10950} \\ A=9838.05 \end{gathered}[/tex]Answer:
[tex]A(30)=9838.05[/tex]