Question 1. Sally, a UTM student, rents a room at a rate of $1300 per month starting in September 1, 2023 and plans to live there for 4 consecutive years. The landlord increases the rent by 2.5% every twelve months. Also on September 1, 2023, Sally receives her student loan disbursement of $20,000, and she plans to use this amount exclusively for rent payments. (a) How much money in total will Sally pay for rent throughout the 4 consecutive years? (b) If Sally receives $20,000 every September in student loans for all 4 years, how much money will she have left over for other expenses over the four years, after paying her rent? Question 2. A new kind of savings account at your bank earns interest in the following way: The account earns interest at a rate of r at the end of every 6-month period; and The account earns interest at a rate of s at the end of every 4-month period. (Note: These rates are not APRs.) In other words, assuming an initial deposit on January 1, the account first earns r in interest at the end of June, then again in December, and so on; while it first earns s in interest at the end of April, then again in August, and so on. Suppose that you make a deposit of P dollars into this account on January 1, 2024, and another deposit of P dollars on January 1, 2025. Assume that you are only allowed to withdraw at the end of every 12-month period. (a) Write an expression that represents the future value S of the account on January 1, 2029. Your answer may depend on r, s, and/or P. (b) Use (a) to compute the amount P required so that the account has S = $10,000 after 5 years. Your answer may depend on r and/or s. (c) Instead of $10,000, suppose you wanted to triple your initial deposit P instead. How many years do you need to wait for the account to grow to three times the initial deposit P? Your answer may depend on r, s, and/or P.