You wish to have $$200,000$ at the end of twenty years. In the last five years, you withdraw $$1,000$ annually at a rate of $3\mathrm{.}8\%$ compounded quarterly. During the middle ten years, you contribute $$500$ monthly at a rate of $2\mathrm{.}8\%$ compounded semi$-$annually. Given this information, determine the initial deposit that has to be made at the start of the first five years at a rate of $4\%$ compounded monthly.