Derek plans to retire on his $65$th birthday. However, he plans to work part$-$time until he turns $71\mathrm{.}00.$ During these years of part$-$time work, he will neither make deposits to nor take withdrawals from his retirement account. Exactly one year after the day he turns $71\mathrm{.}0$ when he fully retires, he will begin to make annual withdrawals of $ $130,574\mathrm{.}00$ from his retirement account until he tums $88\mathrm{.}00.$ He he will make contributions to his retirement account from his $26$th birthday to his $65$th birthday. To reach his goal, what must the contributions be$?$ Assume a $8\mathrm{.}00\%$ interest rate.