College Costs The average annual cost of college at 4 -year...

College Costs The average annual cost of college at 4 -year private colleges was $30,094 in the 2013-2014 academic year. This was a 3.8% increase from the previous year. (a) If the cost of college increases by 3.8% each year, what will be the average cost of college at a 4 -year private college for the 2033-2034 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 2015 to pay for 1 year of the cost of college at a 4-year private college for an incoming freshman in 2033?

College Costs The average annual cost of college at 4 -year private colleges was $30,094 in the 2013-2014 academic year. This was a 3.8% increase from the previous year.
(a) If the cost of college increases by 3.8% each year, what will be the average cost of college at a 4 -year private college for the 2033-2034 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 2015 to pay for 1 year of the cost of college at a 4-year private college for an incoming freshman in 2033?

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Key Concepts

Exponential Growth

Exponential growth describes a process where a quantity increases by a constant percentage each period, leading to a rapid rise over time. This concept is applied when calculating future costs, such as college expenses, by applying a growth factor repeatedly over several years.

Time Value of Money

The time value of money is a fundamental financial principle that emphasizes the importance of the timing of cash flows. It reflects the idea that a dollar today is worth more than a dollar in the future, which is crucial when determining how much to invest now to meet future financial obligations like college payments.

Continuous Compounding

Continuous compounding is an interest calculation method in which the frequency of compounding is effectively infinite, leading to the use of the exponential function. The formula A = P * e^(rt) is used to calculate the future value of an investment compounded continuously, and it is essential for evaluating investment growth in savings plans.

Exponential Functions

Exponential functions are mathematical expressions in which a constant base is raised to a variable exponent. They are essential tools for modeling scenarios involving exponential growth or decay, such as predicting future college costs or the accumulation of funds in an investment account.

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