Problem 3. [13 points] Diane is an accountant. She is 29 years old and expects to work 36 more years. Her current salary is $150,000 (paid at the end of the year), which she expects to grow at a constant rate of 3% per year. The discount rate is 5%. a) What is the present value of Diane's future income stream based on her current salary? b) Diane is unhappy with her current work and is considering doing a five-year PhD in psychology to pursue her life-long dream of becoming a psychologist. For simplicity, assume the PhD starts today (i.e. t = 0). As a PhD, she would receive $35,000 scholarship per year at the beginning of the academic year with no other costs or fees. If Diane pursues the PhD, she expects to get a job right after graduation at NYU Langone Hospital as a resident psychologist. The job entails a sign-up bonus of $25,000 immediately when she starts the job and a starting salary of $160,000 (paid at the end of the year). Diane expects this salary to grow at a rate of 6% annually. Regardless of whether she pursues the PhD or stays in her current job, Diane expects to retire in 36 years from today. Does it pay for Diane to do a PhD