Algebraically manipulating the formula, by making the principal P the subject of the formula, we have;
[tex]P=\frac{FV}{(1+r)^t}[/tex]Given:
[tex]\begin{gathered} FV=\text{ \$8,000} \\ t=5\text{years} \\ r=6\text{ \% =}\frac{6}{100}=0.06 \\ \end{gathered}[/tex]Substituting all these values in the newly generated formula, we have;
[tex]\begin{gathered} P=\frac{FV}{(1+r)^t} \\ P=\frac{8000}{(1+0.06)^5} \\ P=\frac{8000}{1.06^5} \\ P=\frac{8000}{1.338} \\ P=\text{ \$5978.07} \end{gathered}[/tex]Therefore, the principal that needs to be deposited in the bank is $5978.07 to the nearest cent
