Question

A student who will soon receive her BS degree is contemplating continuing her education by
working toward an MS degree in a one year program immediately after her graduation.
She estimates that her earnings for the next 5 years with only a BS degree will be $40,000 per year. Without
the MS degree, after those initial 5 years, she will start to earn monthly salaries that last forever. For each
of these infinitely many years, she estimates that each year her salary will be $A per month for the first 6
months (January through June) and $2A per month for the next 6 months (July through December) if she
does not stay for an MS degree
If she can get an MS degree, her earnings would be $48,000 per year for the subsequent 4 years of obtain-
ing her MS degree (i.e., for years 2, 3, 4 and 5). But her earnings while working on the MS degree (year 1)
will be negligible and her additional annual expenses during her MS education (year 1) will be $12,000. If
she receives an MS degree, after those four initial years, each year her monthly salary will be $A + x for
the first 6 months and $2A + 2x for the following 6 months. She will earn these monthly salaries again forever.
For an annual effective interest rate of 10% compounded monthly, find the value of x for which the extra
investment in MS education will pay for itself.

Answer 1

please comment for doubts

10% 0.008333333 rate for BS degree for MS degree time amount [email protected]% amount*PVF time 12 40,000 0.90524834 36209.93 24 40,000 0.819474557 32778.98 36 40,000 0.741827982 29673.12 48 40,000 0.671431999 26857.28 60 40,000 0.607788591 24311.54 TOTAL 149830.9 6 0.951426524 (for perpetuity) 6 0.951426524 1.902853 (0.9514*2) 2.85428 (0.9514+1.9028) amount PVF amount*PVF 12 - 12000 0.905248 -10863 24 48000 0.819475 39334.78 36 48000 0.741828 35607.74 48 48000 0.671432 32228.74 60 48000 0.607789 29173.85 125482.1 equation1 equation 2 125482+2.854*(A+X) 149830+ A*2.854 equating both equations X= 8531.44 so at $8531.4, investment will pay for itself

thank you