You are retiring today. You are looking into a retirement plan that offers to pay $$10,000$ per year starting next year $($in year $1)$ and that makes $50$ annual payments. The plan will also increase the annual payment by $2\%$ each year. What is the value of this plan today if the discount rate is $8\%?$

$$157,102\mathrm{.}01$

$$169,670\mathrm{.}17$

$$139,753\mathrm{.}98$

$$145,832\mathrm{.}82$