Martin wants to accumulate $$150,000$ saved up in $5$ years, and he plans to make investments as follows:

I. $$30,000$ in $1$ year

II$.$ $$50,000$ in $2$ years, $3$ months

III. A third investment in $3$ years, $6$ months

Martin will also require a withdrawal of $$15,000$ at the end of $3$ years for personal reasons. Suppose all his investments earn $2\mathrm{.}95\%$ compounded monthly. Determine the size of his third investment.