At a nominal interest rate of $i^{(12)}=8\%$ compounded monthly, the effective interest rate per month is $i_m=\frac{i^{(12)}}{12}=0.67\%$. Let $L=100,000$. Without extra payment we have for $n=12\times 30=360$ months
$$
L=P\,a_{\overline{n}|i_m}\quad\Longrightarrow P=\frac{L}{a_{\overline{n}|i_m}}=\frac{100,000}{a_{\overline{360}|0.67\%}}=\frac{100,000}{136.28}=733.76
$$
With an extra monthly payment $Q=100$ we have a periodic payment $P+Q=833.76$.
Then we can find the outstanding loan balance $B_t$
$$
B_{t}=L(1+i_m)^{t}-(P+Q)\,s_{\overline{t}|i_m}
$$
and at $t=120$ we have
$$
B_{120}=\overbrace{100,000\times\underbrace{(1+0.67\%)^{120}}_{2.22}}^{221,964.02}\;-\,\overbrace{833.76\times\underbrace{\,s_{\overline{120}|0.67\%}}_{182.95}}^{152,533.92}=69,430.10
$$
Without the extra payment the OLB would be
$$
B_{t}=L(1+i_m)^{t}-P\,s_{\overline{t}|i_m}
$$
and at $t=120$ we would have
$$
B_{120}=\overbrace{100,000\times\underbrace{(1+0.67\%)^{120}}_{2.22}}^{221,964.02}\;-\,\overbrace{733.76\times\underbrace{\,s_{\overline{120}|0.67\%}}_{182.95}}^{134,239.32}=87,724.70
$$
Using the prospective method we have
$$
B_t=P\,a_{\overline{n-t}|i_m}\quad\Longrightarrow\; B_{120}=733.76\,a_{\overline{240}|0.67\%}=733.76\times 119.55=87,724.70
$$
that is obviously equal to the value founded with the retrospective method.
With an extra payment we will shorten the length $n$ of the loan repayment to a new $N$
$$
L=(P+Q)\,a_{\overline{N}|i_m}=(P+Q)\frac{1-(1+i_m)^{-N}}{i_m}
$$
and then solving for $N$
$$
N=-\frac{\log\left(1-i_m\frac{L}{P+Q}\right)}{\log(1+i_m)}=241.9084704\approxeq 242
$$
that is the lenght of the loan $n=360$ has been shortened to $N=240$ if we make an extra payment.
Using the retrospective method we have
$$
B_t=(P+Q)\,a_{\overline{N-t}|i_m}\quad\Longrightarrow B_{120}=833.76\,a_{\overline{122}|0.67\%}=833.76\times 83.27=69,430.10
$$
