Suppose r, s, t > 0 are interest rates, and compounding interest is applied at the end of each month according to the following scheme: At the end of the first month we compound with an interest rate r, at the end of the second month we compound with an interest rate s, and at the end of the third month we compound with an interest rate t. After this, the cycle begins again. (a) If R dollars is invested at the beginning of the first year, determine the return on investment after two years. (b) You are saving to make a payment of S dollars the end of August in the second year. Determine the amount of money that you must put away on January 1st of the first year, using the above compounding scheme, to ensure that you can cover this payment. (c) Today is January 1st of the first year, and you have taken out a loan of L dollars, amortized over the next three months. Interest is applied according to the above interest scheme. At the end of January, February, and March, you must make payments on this loan. What are your payments? Write your answer in terms of L, r, s, and t. (d) Now suppose you amortized the same loan of L dollars over three years, and are making payments of A dollars monthly. What is the principal remaining on the loan at the beginning of August in the third year? Write your answer in terms of L, A, r, s, and t.