Chapter 5.7, Problem 53AYU

College Costs The average annual cost of college at 4-year private colleges was $\$31,231$ in the 2014-2015 academic year. This was a $3.7\%$ increase from the previous year.

Source: The College Board

(a) If the cost of college increases by $3.7\%$ each year, what will be the average cost of college at a 4-year private college for the 2034-2035 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 2016 to pay for 1 year of the cost of college at a 4-year private college for an incoming freshman in 2034?

To determine

To find: College Costs The average annual cost of college at 4-year private colleges was $\$31,231$ in the 2014-2015 academic year. This was a $3.7\%$ increase from the previous year.

a. If the cost of college increases by $3.7\%$ each year, what will be the average cost of college at a 4-year private college for the 2034-2035 academic year?

Answer to Problem 53AYU

Solution:

a. $64,589.37$

Explanation of Solution

Given:

$P=\$31,231, r=3.7\%=0.037$

Calculation:

a. $t=20$ years $n=1$

$A=P{\left(1+\frac{r}{n}\right)}^{nt}$

$A=31231{\left(1+\frac{0.037}{1}\right)}^{1\left(20\right)}$

$=31231{\left(1+\frac{0.037}{1}\right)}^{20}$

$=\$64,589.37$

To determine

To find: College Costs The average annual cost of college at 4-year private colleges was $\$31,231$ in the 2014-2015 academic year. This was a $3.7\%$ increase from the previous 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 2016 to pay for 1 year of the cost of college at a 4-year private college for an incoming freshman in 2034?

Answer to Problem 53AYU

Solution:

b. $45,062.23$

Explanation of Solution

Given:

$P=\$31,231, r=3.7\%=0.037$

Calculation:

b. In 2034, College fees is $\$64,589$ $r=2\%=0.02$

$A=P{e}^{rt}$

$64,589=P{e}^{0.02\left(18\right)}$

$64,589=P{e}^{0.36}$

$64,589=P\left(1.433329\right)$

$P=\frac{64589}{1.433329}$

$=45,062.23$