MAKE SURE YOU WRITE IN PROPER MATH LANGUAGE EXPLAING ALL STEPS LIEK YOU ARE TEACHING IT TO SOMEONE. PLEASE HELP

Before continuing, ensure that you read the Expectations on Student Writing. Poorly written assignments, even those whose content is ostensibly correct, will receive a poor mark or a mark of zero. If you are uncertain as to what qualifies as good writing, do not hesitate to seek out the advice of a course instructor or teaching assistant. 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