Suppose you have just started $26$th 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 $2\mathrm{.}4\%$ each year $(0\mathrm{.}2\%$ per month$).$ You

want to consume $$2,500$ per month when you retire with the growth rate of $0\mathrm{.}2\%$ 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.