Question: Optimal Consumption and Savings

It is January 1st, 2020, you are (just turned) 25 years old and are earning $7,000 per month, (with payments received at the end of each month). Moreover, each monthly payment is adjusted for inflation, i.e. the monthly (nominal) growth rate of your wages is equal to the monthly rate of inflation. You determine that your job is safe enough to warrant a nominal valuation rate of 4% (APR). You estimate that inflation will be 1.8% (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 $1,700 each month in order to survive (i.e. your current implicit liabilities are equal to $1,700 per month). Assume that you will live to age 100, retire on your 65^th birthday (both with certainty) and that you want a constant real standard of living.

Part A(4pts): What is your optimal savings rate for the current month?

Part B(3pts): How much financial capital will you have when you start retirement?