Chapter 7, Problem 5P

(a)

To determine

Determine whether Person J goes to junior college or work.

Explanation of Solution

According to the given information, there are two options.

Option 1:

If Person J plans to go to work, the earning will be $20,000 per year. This means, after 5 years, the total earning will be $1 00,000$\left(\$20,000\times 5\right)$. Person J’s yearly expense with zero interest is $15,000. That is, after 5 years, the total expense is $75,000$\left(\$15,000\times 5\right)$. Therefore, if Person J opts the 1^st option, that is, ‘goes to work’, then the savings after 5 years will be $25,000 $\left(\$100,000-\$75,000\right)$. 

Option 2:

If Person J plans to go to junior college, the earnings after 2 years will be $38,000 per year. This means, after 5 years, the total earning will be $114,000$\left(\$38,000\times 3\right)$. Person J’s yearly expense is $15,000 plus the course fee 6000 per year for two years. That is, after 5 years, the total expense is $87,000$\left(\left(\$15,000\times 5\right)+\left(\$6000\times 2\right)\right)$. Thus, if Person J opts the 2^nd option, that is, ‘goes to junior college’, then the savings after 5 years will be $27,000$\left(\$114,000-\$87,000\right)$.

Since Person J’s objective is to maximize the savings, he will opt the second option. That is, goes to junior college.        

(b)

To determine

Determine whether Person J goes to junior college or work, if the earnings increase.  

Explanation of Solution

If Person J‘s earning is $23,000 per year, after 5 years, the total earnings will be $115,000$\left(\$23,000\times 5\right)$ and as mentioned in part ‘a’, Person J’s yearly expense is still $75,000. Then, the savings after 5 years will be $40,000$\left(\$115,000-\$75,000\right)$. Since Person J’s objective is to maximize the savings and the savings from the second option is still $27,000 (explained in part ‘a’), Person J will opt the 1st option. That is, goes to work.

(c)

To determine

Determine whether person J goes to junior college or work, if the tuition and book costs increase.

Explanation of Solution

As explained in part ‘a’, Person J’s savings from the 1^st option is $25,000 and the savings from the second option is $27,000.  If the tuition fee and book costs increase from $6,000 to $8,000, the total cost after 5 years become $91,000$\left(\left(\$15,000\times 5\right)+\left(\$8000\times 2\right)\right)$. Thus, if Person J opts the 2^nd option, that is, ‘goes to junior college’, then the savings after 5 years will be $23,000$\left(\$114,000-\$91,000\right)$, which is less than the savings from the 1st option.

Since Person J’s objective is to maximize the savings, he will opt the 1st option. That is, goes to work.

(d)

To determine

Determine whether Person J goes to junior college or work with the 10% interest rate.

Explanation of Solution

As mentioned in part ‘a’, the savings of the 1^st option is $25,000 after 5 years. That is, $5,000 $\left(25,000/5\right)$ is per year savings with zero interest rate. If the interest rate is 10%, then the value of $5,000 after 5 years can be calculated using the compound method as follows:

In 1^st year, the savings is $5,000.

In 2^nd year, the savings is $5,500 (10% 5,000 plus 5,000).

In 3^rd year, the savings is $6,050 (10% 5,500 plus 5,500).

In 4^th year, the savings is $6,655 (10% 6,050 plus 6,050).

In 5^th year, the savings is $7,320.50 (10% 6,655 plus 6,655).

If Person J plans to opt option 2, that is, ‘goes to junior college’, then at the end of the 1^st year, the total cost is $21,000$\left(\$15,000+\$6,000\right)$. After 5 years, the total cost with 10% interest can be calculated as follows:

$\begin{array}{c}{\text{Total cost}}_{\text{After 5 years}}=\text{Cost per year}\times {\left(1+\text{r}\right)}^{\text{n}}\\ =\$21,000\times {\left(1+0.1\right)}^4\\ =\$30,746\end{array}$

Thus, if Person J opts the second option, the total cost after 5 years with 10% interest will be $30,746. After 2 years, Person J will complete the course and enter into the world of work. Thus, the total cost for the reaming 3 years can be calculated as follows:

$\begin{array}{c}{\text{Total cost}}_{\text{After 3 years}}=\text{Cost per year}\times {\left(1+\text{r}\right)}^{\text{n}}\\ =\$21,000\times {\left(1+.10\right)}^3\\ =\$27,951\end{array}$

Thus, after entering into the job, the total cost will be $27,951.

In years 3 to 5, the earnings of Person J will be $38,000 per year and he spends $15,000 as expense. Thus, the savings will be $23,000 per year. At the end of 5 years, the value of these savings can be calculated as follows:

$\begin{array}{c}{\text{Savings}}_{\text{At the end of 5 year}}={\text{Savings in 1}}^{\text{st}}\text{year}+{\text{Savings in 2}}^{\text{nd}}\text{year}+{\text{Savings in 2}}^{\text{nd}}\text{year}\\ =\text{\$23,000}+\left(\text{\$23,000}\times \text{1}+.10\right)+{\left(\text{\$23,000}\times \text{1}+.10\right)}^2\\ =\text{\$23,000}+\$25,300+\$27,830\\ =\$76,130\end{array}$ 

Thus, at the end of 5 years, the value of these savings will be $76,130.

Now, subtract the value of debts of Person J from the savings as follows:

$\begin{array}{c}\text{Assets}=\text{Savings}-\text{Debts}\\ =\text{\$76,130}-\left(30,746+27,951\right)\\ =\$17,433\end{array}$

Therefore, the saving yields $17,433 in assets at the end of five years. This amount is less if Person J skips junior college. Since Person J’s objective is to maximize the savings, he will opt the 1st option. That is, goes to work.