Question 2 A student who will soon receive her BS degree is contemplating continuing her education...

 

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Question 2 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 SA 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. Question 2 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 SA 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.

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