The parents of a newborn baby would like to put money away today to cover $100\%$ of the child$$s expected total $4-$years of college tuition. The first tuition payment is due exactly $18$ years from today, and the next three payments are due at the end of years $19,20$ and $21.$ Suppose that the parents estimate that the cost of tuition will be $$86,000$ per year for the first three years, but that the fourth year$$s tuition will be $$96,000.$ Which comes closest to the amount of money that needs to be set aside today if the interest rate is $6\%?$

A$.$

$ $104,719$

B$.$

$ $136,639$

C$.$

$ $16,857$

D$.$

$ $113,608$

E$.$

$ $198,781$