Jack and Joe are close friends. They both graduated in January 2011. Right after graduation, they started their professional career in the same company with same amount of after-tax pay: $4,990.05 per month. At the same time, they both purchased a house in the same neighborhood for the same price: $440,000.00. They both paid $40,000 out of packet and got a mortgage for the remaining $400,000 with the same APR of 4.5%, compounded monthly. The mortgage is to be paid off in 360 equal monthly payments. Furthermore, Jack sold his car and used the proceeds as the down payment for a brand- new Cadillac. He financed his Cadillac with a 5-year loan of $55,000 with an APR of 6%, compounded monthly. Joe, however, kept his old car. During the first 5 years after graduation, Jack spent $1,900 per month on all his living expenses other than the mortgage and auto loan payments. Joe, however, spent more cautiously and averaged $1,400 per month. After 5 years, both Jack and Joe got a raise, and their after-tax monthly pay increased to $6,176.70. Being a car lover, Jack immediately sold his car, used the proceeds as the down payment for a Tesla that her financed with a 5-year auto-loan of $75,000 with an APR of 6%, compounded monthly. Joe, however, decided to keep his old car for another five years. Moreover, right after the raise, Jack started to live more lavishly. During the last five years, he averaged $2,700 per month on his living expenses. Joe, also, became less conservative about money and averaged a living expense of $2,000 per month. During all these 10 years, at the end of each month, Joe invested his monthly savings in the S&P 500 index and kept it there. During these 10 years, S&P 500 index generated an average monthly return of 1.1333%.

4: Show that Jack have been unable to saving any money during these 10 years. That is, show that for both of the 5-year periods (Jan. 2011 - Dec. 2016 and Jan. 2017 - Dec. 2021) Jacks total monthly expenses have been equal to his monthly earnings.