Richard and Mary wants to provide full funding for their $3$ year old daughter who is expected to start college when she is $18.$ The current annual cost of a $4$ year college is $$38,000$ which is expected to increase by $3\mathrm{.}5\%$ per year. They expect to earn $5\%$ on their investment. Calculate the total cost $($lump sum amount$)$ required by them to fund $4$ years of college when their daughter turns $18.$

Group of answer choices

$$254,653$

$$242,811$

$$245,687$

$$249,245$