Chapter 9.7, Problem 1CYP

To determine

The cost of tuition for college in 2015

Answer to Problem 1CYP

The cost of tuition for college in 2015 is $\$21482.25$

Explanation of Solution

Given information:

A college’s tuition has risen 5% each year since 2000 and if the tuition in 200 was $10850

So the value is

  $\begin{array}{l}P=10850\\ t=t\\ r=5\%\\ =\frac{5}{100}\\ =0.05\end{array}$

Concept used:

• The formula for compound interest: $A=P{\left(1+\frac{r}{n}\right)}^{nt}$
• Where
  $\begin{array}{l}A=\text{final}\text{amount}\\ P=\text{principal}\text{balance}\\ r=\text{rate}\text{of}\text{interest}\\ n=\text{number}\text{of}\text{times}\text{intrest}\text{applied}\text{per}\text{time}\text{period}\\ t=\text{number}\text{of}\text{time}\text{periods}\end{array}$

Calculation:

To find the equation, for the amount of tuition t years after 2000 is as below:

  $\begin{array}{c}A=P{\left(1+\frac{r}{n}\right)}^{nt}\\ =10850{\left(1+0.05\right)}^t\\ A=10850{\left(1.05\right)}^{14}\end{array}$

Thus, the equation is $A=10850{\left(1.05\right)}^{14}$

So the cost of tuition for college in 2015 as below

  $\begin{array}{c}A=10850{\left(1+0.05\right)}^t\\ =10850{\left(1+0.05\right)}^{14}\\ =10850{\left(1.05\right)}^{14}\\ 10850\times 1.97\\ =21482.25\end{array}$

Thus, the cost of tuition for college in 2015 is $\$21482.25$