The Time Value of an Annuity

Question #2: Suppose you have just started 26th year of your life, you plan to retire at the end of age 65, and you expect to live until the end of 85 (working for 40 full years and being retired for 20 years). You are currently earning $48,000 per year (paid monthly at the end of each month) which grows 2.4% each year (0.2% per month). You want to consume $2,500 per month when you retire with the growth rate of 0.2% per month. The plan is to save a fixed percentage of your income each month to meet your retirement needs.

Part A: Assuming an interest rate of 3% (annual percentage rate, compounded monthly), what is your saving rate? Part B: Assuming an interest rate of 6% (annual percentage rate, compounded monthly), what is your saving rate? Part C: How can you explain the change in saving rate in response to the change in interest rate? Discuss.

PLEASE SHOW ALL THE WORKINGS.