You have just opened a savings account which pays monthly interest at a rate of \\( j_{12} \\) \=5.5 p.a. You wish to accumulate \\( \\$ 20,000 \\) by depositing the same amount into the account at the end of each month, for 2 years, starting in a month's time. a) Determine the required size for the monthly deposit, R. Apply a sanity check. b) Construct a sinking fund table showing 24 deposits with a fixed interest rate of \5.5. Describe and apply a sanity check to your table. c) Suppose that the interest rate is renewed every three months (quarterly) over the course of the two years as follows: If you maintain the same monthly deposit of \\( \\mathrm{R} \\) determined in part \\( \\mathrm{a} \\) ), find the size of your sinking balance after two years. Will you meet your target of \\( \\$ 20,000 \\) ? Describe and apply a sanity check for your answer. d) Construct a sinking fund table showing 24 deposits with the variable interest rate. Describe and apply a sanity check to your table