We are asked to find the principal for an amount compounded quarterly. Let's remember the formula for a future compounded quarterly:
[tex]A=P(1+\frac{r}{4})^{4t}[/tex]We solve for P:
[tex]\frac{A}{(1+\frac{r}{4})^{4t}}=P[/tex]We are given the following values:
[tex]\begin{gathered} A=5000 \\ r=0.03 \\ t=2 \end{gathered}[/tex]Replacing we get:
[tex]\frac{5000}{(1+\frac{0.03}{4})^{(4)(2)}}=P[/tex]Solving the operations:
[tex]4709.88=P[/tex]Therefore, the initial value must be $4709.88
