Answer
$\$ 105.38$
Work Step by Step
A sinking fund is an account earning compound interest into which you make periodic deposits. $\\$
$FV=PMT\displaystyle \cdot\frac{(1+i)^{n}-1}{i}, \quad PMT=FV\cdot\frac{i}{(1+i)^{n}-1}$
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given: $\\$
$t=5$ years,
annual rate: r =$0.05$
m=$12 \ \ \ $compounding periods per year,
$\displaystyle \mathrm{i}=\frac{r}{m}=\frac{0.05}{12} \ \ $(rate per compounding period$)$
$n=mt=60 \ \ $(total number of periods)
During this time, the initial $PV=10,000$ will grow to
$FV_{0}=PV(1+\displaystyle \frac{r}{m})^{mt}=10,000(1+\frac{0.05}{12})^{60}\approx 12833.59$
which leaves
$FV=20,000-12,833.59=7166.41$
for the sinking fund
$PMT=FV\displaystyle \cdot\frac{i}{(1+i)^{n}-1}$
$=7166.41\displaystyle \cdot\frac{\frac{0.05}{12}}{(1+\frac{0.05}{12})^{60}-1}$
$\approx$105.379003107