The formula relating future value and present value is given as:
[tex]FV=PV(1+r)^n[/tex]Where,
• FV is the future value
,• PV is the present value
,• r is the rate of interest
,• n is the number of periods interest held.
Rewrite the rate as a decimal:
[tex]r=9\frac{1}{2}\%=9.5\%=0.095[/tex]Substitute FV=8600, r=0.095, n=5 into the formula:
[tex]8600=PV(1+0.095)^5[/tex]Simplify the equation and solve for PV:
[tex]\begin{gathered} 8600=PV(1.095)^5 \\ PV=\frac{8600}{(1.095)^5}\approx5462.96 \end{gathered}[/tex]Hence, the present value is about $5,462.96.
