Suppose that a young couple has just had their first baby and they wish to ensure that enough money will be available to pay for their child's college education. Currently, college tuition,

books, fees, and other costs average $$12,700$ per year. On average, tuition and other costs have historically increased at a rate of $3\%$ per year.

Assuming that college costs continue to increase an average of $3\%$ per year and that all her college savings are invested in an account paying $7\%$ interest, then the amount of money she will

need to have available at age $18$ to pay for all four years of her undergraduate education is closest to

A$.$ $$81,754$

B$.$ $$57,228$

C$.$ $$98,105$

D$.$ $$40,877$