The average annual cost of college at 4-year private...

The average annual cost of college at 4-year private colleges was $\$ 34,740$ in the $2017-2018$ academic year. This was a $3.6 \%$ increase from the previous year. (a) If the cost of college increases by $3.6 \%$ each year, what will be the average cost of college at a 4 -year private college for the $2037-2038$ 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 2019 to pay for 1 year of the cost of college at a 4-year private college for an incoming freshman in $2037 ?$ Source: The College Board

The average annual cost of college at 4-year private colleges was $\$ 34,740$ in the $2017-2018$ academic year. This was a $3.6 \%$ increase from the previous year.
(a) If the cost of college increases by $3.6 \%$ each year, what will be the average cost of college at a 4 -year private college for the $2037-2038$ 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 2019 to pay for 1 year of the cost of college at a 4-year private college for an incoming freshman in $2037 ?$
Source: The College Board

Key Concepts

Time Value of Money

The time value of money is the financial concept that money available today is more valuable than the same amount in the future due to its potential earning capacity. This principle underpins both the calculation of future costs through growth rates and the present investment required in a savings plan to cover anticipated future expenses.

Exponential Growth

Exponential growth describes the process in which a quantity increases by a constant percentage over equal time intervals. In the context of the rising college costs, a fixed rate of 3.6% per year leads to a compounding effect, causing the total cost to escalate significantly over time.

Compound Interest

Compound interest is the principle that not only does the initial principal earn interest, but the accumulated interest also earns interest in subsequent periods. This concept is applied when calculating the future value of college costs with a yearly increase, as each year’s increase builds upon the previous year's total.

Continuous Compounding

Continuous compounding is a form of interest calculation where the interest is added to the principal an infinite number of times per period, modeled mathematically by the exponential function. In financial planning, such as calculating the amount needed in a savings plan at 2% continuous compounding, this method is used to determine the present value required to meet a future expense.

Transcript

Please give Ace some feedback