Question #3: Optimal Consumption and Savings

It is January 1st , 2020, you are (just turned) 22 years old and are earning $3,500 per month, (with payments received at the end of each month). Each monthly payment is growing at a nominal rate of 3.5% per year, annual compounding. You determine that your job is safe enough to warrant a nominal valuation rate of 5% (APR). You estimate that inflation will be 2.5% (APR) for the foreseeable future. In addition, you recently paid off all your debt, and as a result have zero financial capital. You have carefully determined that you require $1,500 each month in order to survive (i.e. your current subsistent consumption is equal to $1,500 per month). Assume that you will die when you turn 95, retire on your 65th birthday (both with certainty) and that you want a constant real standard of living.

Part A: What is your optimal savings at the end of the current month (i.e. on January 31st, 2020)?

Part B: How much financial capital will you have when you start retirement?