Question

1. Suppose students live for three periods and have a discount rate of 6%. A student is trying to decide whether or not to attend college. If the student decides to not attend college, they will earn $28, 000 at the end of the first period, $32, 000 at the end of the second period, and $38, 000 at the end of the third period. If the student attends college, then tuition is due at the beginning of the first period $10,000, the student earns $55,000 at the end of the second period. If the student elects to go to college, then what is the minimum amount that they must earn at the end of the third period.

(Please do not just copy other expert's answer on CHEGG, it is wrong. Please write your own answer.)

Answer 1

ANSWER:

I = 6%

N = 3 years

pw if student doesn't decide to attend the college = earnings in 1st year(p/f,i,n) + earnings in 2nd year(p/f,i,n) + earnings in 3rd year(p/f,i,n)

pw = 28,000(p/f,6%,1) + 32,000(p/f,6%,2) + 38,000(p/f,6%,3)

pw = 28,000 * 0.9434 + 32,000 * 0.89 + 38,000 * 0.8396

pw = 26,415.2 + 28,480 + 31,904.8

pw = 86,800

so the pw of not attending college is $86,800

pw if student attends college = earnings in 1st year(p/f,i,n) + earnings in 2nd year(p/f,i,n) + earnings in 3rd year(p/f,i,n)

pw = -10,000(p/f,6%,1) + 55,000(p/f,6%,2) + earnings in 3rd year(p/f,6%,3)

pw = -10,000 * .9434 + 55,000 * 0.89 + earnings in 3rd year * 0.8396

pw = - 9,434 + 48,950 + earnings in 3rd year * 0.8396

pw = 39,516 + earnings in 3rd year * 0.8396

In order to find out the minimum amount that they must earn at the end of the third period, we will equate the pw equal of both the scenarios.

86,800 = 39,516 + earnings in 3rd year * 0.8396

86,800 - 39,516 = earnings in 3rd year * 0.8396

47,284 = earnings in 3rd year * 0.8396

earnings in 3rd year = 47,824 / 0.8396

earnings in 3rd year = 56,317.29

so the minimum earnings has to be $56,317.29