The average annual cost of college at 4-year private colleges was $38,070 in the 2021–2022 academic year. This was a 2.1% increase from the previous year.

(a) If the cost of college increases by 2.1% each year, what will be the average cost of college at a 4-year private college for the 2041–2042 academic year?

(b) College savings plans, such as a 529 plan, allow individuals to put money aside now to help pay for college later. If one such plan offers a rate of 2% compounded continuously, how much should be put in a college savings plan in 2023 to pay for 1 year of the cost of college at a 4-year private college for an incoming freshman in 2041?