We are given the following information
Investment = $5200
Annual interest rate = 4.2% = 0.042
Final amount = $16,500
Number of years = 27.7 years
Number of compoudings = quartely = 4
The student uses the following model
[tex]V(t)=5200(1.014)^{3t}[/tex]The general formula for compound interest is given by
[tex]V(t)=P(1+\frac{r}{n})^{nt}[/tex]As you can see, the number of compoundings is incorrect (3 vs 4)
The interest rate is also incorrect.
Let us substitute the given values into the above formula
[tex]\begin{gathered} V(t)=P(1+\frac{r}{n})^{nt} \\ V(t)=5200(1+\frac{0.042}{4})^{4\cdot27.7} \\ V(t)=5200(1+0.0105)^{110.8} \\ V(t)=5200(1.0105)^{110.8} \\ V(t)=\$16543.5^{} \end{gathered}[/tex]Therefore, the final amount is approximately $16,543.5
