Question

Joanne has just completed high school and is trying to determine whether to go to junior college for two years or go directly to work. Her objective is to maximize the savings she will have in the bank five years from now. If she goes directly to work, she will earn $20,050 per year for each of the next five years. If she goes to junior college, for each of the next two years she will earn nothing—indeed, she will have to borrow $6,000 each year to cover tuition and books. This loan must be repaid in full three years after graduation. If she graduates from junior college, in each of the subsequent three years, her wages will be $38,050 per year. Joanne’s total living expenses and taxes, excluding tuition and books, equal $15,000 per year. Instructions: Enter your responses as whole numbers. a. Suppose, for simplicity, that Joanne can borrow and lend at 0 percent interest. On purely economic grounds, should she go to junior college or work? After 5 years, the total value of Joanne's savings would be $ if she goes directly to work and $ if she goes to junior college. So, Joanne should go to . b. Does your answer to part a change if Joanne can earn $23,050 per year with only a high school degree? . Joanne should go to , since the total value of Joanne's savings would be $ if she goes directly to work and $ if she goes to junior college. c. What if Joanne’s tuition and books cost $8,000 per year? Joanne should go to , since the total value of Joanne's savings would be $ if she goes directly to work and $ if she goes to junior college. d. Suppose that the interest rate at which Joanne can borrow and lend is 10 percent per year, but she can earn $20,050 with a high school degree. Her tuition and books at college cost $6,000 and her living expenses are $15,000 per year. Savings are deposited at the end of the year they are earned and receive (compound) interest at the end of each subsequent year. Similarly, the loans are taken out at the end of the year in which they are needed, and interest does not accrue until the end of the subsequent year. Now that the interest rate has risen, should Joanne go to college or go to work? Joanne should go to , since the total value of Joanne's savings would be $ if she goes directly to work and $ if she goes to junior college.

Answer 1

Answer ( a) : If Joanne directly goes to work by skipping the Junior College, then :

                        Joanne’s total earnings in five years = $ 20,050 x 5

                                                                                         = $ 100,250

                       Joanne’s total monthly expense is $15,000/ year

                       i.e. in 5 years , Joanne’s expenditure= $ 75,000

Therefore, Joanne’s total savings in 5 years if she goes directly to wok by skipping the Junior college would be                                                     = $100,250 - $75000

                                                                      = $ 25,250

However, if Joanne chooses to go to Junie college , she initially looses $6000/ year for 2 years , i.e.

                                                                    = $12000

From the third year Joanne starts earning 38,050, therefore her total income in next three years

                                                                    = ( $38,050 x 3 ) - $12000

                                                                   = $ 102,150

She her monthly expenditure is $15000, her total net savings = $102,150 – $ 45000 = $ 57,150

Therefore, even though Joanne is having to initially take loan, Joanne should study first in junior college and then start working .

       

Answer (b): Again now, Joanne directly goes to work by skipping the Junior College, then :

                        Joanne’s total earnings in five years = $ 23,050 x 5

                                                                                         = $ 115,050

                       Joanne’s total monthly expense is $15,000/ year

                       i.e. in 5 years , Joanne’s expenditure= $ 75,000

Therefore, Joanne’s total savings in 5 years if she goes directly to wok by skipping the Junior college would be                                                     = $115,050 - $75000

                                                                      = $ 40,050

Therefore, Joan should prefer to study first in junior college and then start working.

Answer ( C ) : If Joanne’s tuition and other fees is $8000 per year, she initially loses $8000/ year for 2 years , i.e.

                                                                    = $16000

From the third year Joanne starts earning 38,050, therefore her total income in next three years

                                                                    = ( $38,050 x 3 ) - $16000

                                                                   = $ 98,150

She her monthly expenditure is $15000, her total net savings = $98,150 – $ 45000 = $ 53,150

Therefore, even if Joanne’s tuition fees and other expenses are high at $ 8000 per year, she should stil prefer to go to Junioe college first.

Answer (d) : if Joanne chooses to go to Junie college , she initially loses $6000/ year for 2 years ( now compounded with 10% as interest rate) :

                                                                    = $ 6000 + (10% of 6000 ) + that amount + 10% of that amount

                                                                    = $ 6600 + $7260

                                                                    = $ 13,860

From the third year Joanne starts earning 38,050, therefore her total income in next three years ( now have compound interest to them )

                                                                    = $38,050 +10% of 38,050 ( compounded for next two years

                                                                   = $ 41,855 + 46,040 + 50,644

                                                                   = $ 138,539 - $ 13860

                                                                  = $ 124,679

Since her monthly expenditure is $15000, her total net savings = $124,679 – $ 45000 = $ 57,150

                                                                                                                  = $ 79,679

Therefore, Joanne initially looses more money owing to paying interest for the borrowings, but she is earning much more at a later stage owing to the interest from her savings, therefore, she should go to Junior college first.

Answer 2

If Joanne directly goes to work by skipping the Junior College, then :

                        Joanne’s total earnings in five years = $ 20,050 x 5

                                                                                         = $ 100,250

                       Joanne’s total monthly expense is $15,000/ year

                       i.e. in 5 years , Joanne’s expenditure= $ 75,000

Therefore, Joanne’s total savings in 5 years if she goes directly to wok by skipping the Junior college would be                                                     = $100,250 - $75000

                                                                      = $ 25,250