For an amount whose interest is compounded quarterly, the formula applied is;
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \text{Where;} \\ P=500,r=0.04,n=4,t=1 \end{gathered}[/tex]Since the cousin pays back in 6 months, then the value of t, which is time, shall be 0.5. Hence, we would have;
[tex]\begin{gathered} A=500(1+\frac{0.04}{4})^{4\times0.5} \\ A=500(1+0.01)^2 \\ A=500(1.01)^2 \\ A=500\times1.0201 \\ A=510.05 \end{gathered}[/tex]The total amount the cousin owes Chelsea is $510.05
