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.