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

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?

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 over equal time intervals. It is often modeled by the formula Future Value = Present Value × (1 + growth rate)^(number of periods), which is useful for estimating future costs or values that increase at a fixed percentage rate each period.

Continuous Compounding

Continuous compounding is a concept where interest is earned constantly, leading to growth modeled by the formula A = P·e^(rt), where P is the initial amount, r is the annual interest rate, and t is time. This method captures the idea of earnings being accrued and reinvested at every moment rather than at discrete intervals.

Time Value of Money

The time value of money is a fundamental principle in finance stating that money available now is worth more than the same amount in the future due to its potential earning capacity. This concept underpins calculations involving both growth over time, as seen with exponential or continuously compounded interest, and discounting future amounts to understand their present value.

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