1. This problem explores quantitatively the effects of inflation on "buying power" of an initial amount of money as prices increase over time; Examples 7 and 13 in section 5.2 of the text illustrate this concept. (a) Xavier deposits $30,000 into an account bearing 2.4% interest compounded quarterly. How much will be in the account in 10 years? (b) After making the deposit, Xavier reads news reports that the inflation rate is expected to average 2.0% during the next five years, and to average 4.0% in the five years following that. If this prediction is correct, what will be the "buying power" of the accumulated amount in his account after those 10 years? (Hint: first calculate the discount due to inflation over the indicated 10 years; then apply it to the accumulated amount. Do not try to adjust the account balance for inflation on a year-by-year basis, there is no need to do so, since we are only interested in the effect over the full ten years.] (c) To counteract this predicted inflation, Xavier proposes to make additional regular quarterly deposits (of equal amounts each time) into his account over the next ten years, and to choose the quarterly deposit amount so that the buying power of his total accumulation in ten years is $30,000 (i.e., he will make extra contributions to make up for inflation, so that he ends up with unchanged buying power after ten years). What will his quarterly contributions need to be? 2. This problem investigates the quantitative differences between saving in advance and borrowing and then repaying. The XYZ Corporation will construct a new bicycle storage facility in 2023. On 1 January of that year, the builder will require payment of the $1,000,000 cost. The company has access to a savings account, bearing 4.8% interest, compounded monthly, and also has access to loan facility offering funding at 4.8%, also compounded monthly. XYZ are contemplating two funding schemes: . Scenario A: The company establishes a sinking fund to accumulate $1,000,000 through 24 monthly deposits between January 2021 and December 2022. . Scenario B: Using its loan facility, the company borrows $1,000,000 on 01 January 2023, and pays off the loan with 24 monthly payments. (a) What is the difference between the total deposits made by the company in Scenario A and the total payments they would make in Scenario B? (Calculate each quantity and then find the difference; there is no good way to calculate this difference directly.] (b) It is suggested a hybrid scenario be employed: that 24 months of contributions be made into the savings account during 2021-2022 so that 24 monthly withdrawals could be made in 2023-2024 to be used as the loan payments in Scenario B. What would the monthly deposit amount need to be so that the balance in the account as of 01 January 2023 would fund exactly the subsequent loan payments? (c) What are the total deposits made by the company in this hybrid approach? How does this compare to the total deposits in Scenario A? How do you explain the difference