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

The average annual cost of college at 4-year private colleges was $\$ 25,143$ in the $2008-2009$ academic year. This was a $5.9 \%$ increase from the previous year. Source: The College Board (a) If the cost of college increases by $5.9 \%$ each year, what will be the average cost of college at a 4 -year private college for the $2028-2029$ 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 $4 \%$ compounded continuously, how much should be put in a college savings plan in 2010 to pay for 1 year of the cost of college at a 4 -year private college for an incoming freshman in $2028 ?$

The average annual cost of college at 4-year private colleges was $\$ 25,143$ in the $2008-2009$ academic year. This was a $5.9 \%$ increase from the previous year. Source: The College Board
(a) If the cost of college increases by $5.9 \%$ each year, what will be the average cost of college at a 4 -year private college for the $2028-2029$ 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 $4 \%$ compounded continuously, how much should be put in a college savings plan in 2010 to pay for 1 year of the cost of college at a 4 -year private college for an incoming freshman in $2028 ?$

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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. In financial contexts, this concept is used to model situations such as rising costs or growing investments, where each year's value is a fixed percentage higher than the previous year's. It is represented mathematically by multiplying the initial value by (1 + growth rate) raised to the number of time periods.

Future Value Calculation

Future value calculation involves determining the value of an investment or expense at a future date by accounting for a growth or increase rate over time. This is a key concept in planning and budgeting, where current amounts are projected forward based on expected rates of inflation or return, enabling strategic decision-making regarding savings or pricing.

Continuous Compounding

Continuous compounding is a financial concept where interest is added to the principal at every moment in time, rather than at discrete intervals. This model uses the exponential function, with the formula A = P * e^(rt), to calculate the future value of an investment or cost. It is particularly useful in modeling situations where growth or decrease happens in a smooth, uninterrupted manner over time.

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