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Question 1. On October 1, 2022 you take out a loan of $20000 from the bank, which offers a promotional rate of 3% (APR) compounded monthly. You agree to make mouthly payments of R for 3 years at the end of each mouth. starting October 31, 2022, so that the last payment is made on September 30, 2025. (a) Compute R (rounded to two decimal places). (b) Using your answer in part (a), compute how much principal remains on the loan on June 1, 2023. (c) On June 1, 2023 the promotional rate ends, and the new rate for the loan becomes 10\% (APR), compotunded monthly. Compute your new monthly payments S starting June 30,2023 , assuming that you still fully pay off the loan on September 30, 2025. (d) The bank offers you another option: you can keep the monthly payments unchanged (so the same as R in part (a)) after the interest rate increase on June 1, 2023. Instead, the amortization period will be extended past the original three years. Determine when the loan will be paid off. Question 2. Your client is considering investing in shares from YSN, KRS, and HSN. As their financial advisor, you offer the customer the following three portfolios: - Portfolio A contains three shares of YSN, five of KRS, and eight of HSN. - Portfolio B contains two shares of YSN, three of KRS, and two of HSN. - Portfolio C contains five shares of YSN, two of KRS, and one of HSN. (a) If your elient buys two units of Portfolio A, two units of Portfolio B, and one unit of Portfolio C, how many shares of KRS will they have in total? (b) Your elient wants exactly 27 shares of YSN, 19 shares of KRS, and 16 shares of HSN; they ask you how many units of each portfolio to buy. Set up a linear system which models this question. You do not need to solve the linear system. (c) Another client approaches you, and they want to purchase the same portfolios so that they have two shares of YSN, five shares of KRS, and three shares of HSN. They set up a similar linear system the same way you did in part (b), but this time they solve the system themselves and get the solution (x,y,z)=(3,5,2). What can you say to this client