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 $ $12$ comma $300$ 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 $\_\_\_\_\_\_$