Answer
$\$ 15,528.23$
Work Step by Step
A sinking fund is an account earning compound interest $\\$
into which you make periodic deposits. $\\$
Let it have an annual rate of r compounded m times per year, $\\$
i = r /m is the interest rate per compounding period. $\\$
If you make a payment of PMT at the end of each period, $\\$
then the future value after t years, or n = mt periods, will be$\\$
$FV=PMT\displaystyle \cdot\frac{(1+i)^{n}-1}{i}\\\\$
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Here, $\\$
$t=10$ years$,\\$
m= $12 \ \ \ $compunding period per year,$\\$
$n=mt=120 \ \ $(number of periods)$\\$
$\displaystyle \mathrm{i}=\frac{r}{m}=\frac{0.05}{12}\approx 0.004167 \ \ $(rate per compounding period)$\\$
$PMT=100\ \ \ $( payment at the end of each period)$\\\\$
$ FV=PMT\displaystyle \cdot\frac{(1+\frac{0.05}{12})^{120}-1}{\frac{0.05}{12}}\approx$15528.2279446
