Answer
$\$ 6757.41$
Work Step by Step
A sinking fund is an account earning compound interest into which you make periodic deposits.
Here, $\\\\$
r$=0.0475 \ \ \ \ ...$annual rate$, \\\\$
m$=12 \ \ \ \ $ ...compounding periods per year, $\\\\$
i = r /m$=\displaystyle \frac{0.0475}{12} \ \ \ \ ...$ interest rate per compounding period. $\\\\$
If you make a payment of PMT$=100 \\\\$
at the end of each period, then the future value $\\\\$
after $t=5$ years, $\\\\$
or, $n = mt =12(5)=60 \ \ \ \ ...$ periods, $\\\\$
will be$\\\\$
$FV=PMT\displaystyle \cdot\frac{(1+i)^{n}-1}{i}\\\\$
$=100\displaystyle \cdot\frac{(1+\frac{0.0475}{12})^{60}-1}{\frac{0.0475}{12}}\approx$6757.40572075
