Christopher plans to make regular savings contributions of $$4,090\mathrm{.}00$ per year for $9$ years. His first regular savings contribution is expected in $1$ year. In addition, he plans to make a special savings contribution of $$10,470\mathrm{.}00$ in $5$ years. Christopher expects to earn $13\mathrm{.}96$ percent per year. How much money does Christopher expect to have in $9$ years?

$$51,599\mathrm{.}14($plus or minus $10$ dollars$)$

$$54,064\mathrm{.}28($plus or minus $10$ dollars$)$

$$83,335\mathrm{.}73($plus or minus $10$ dollars$)$

$$37,782\mathrm{.}36($plus or minus $10$ dollars$)$

none of the answers are within $10$ dollars of the correct answer