Solving for Time

Question #4: Suppose you have just started 21st year of your life, you plan to retire at the end of age 65, and you expect to live until the end of 90 (working for 45 full years and being retired for 25 years). You currently have a constant earning of $50,000 per year (paid at the end of the year). The plan is to save 10% of your income each year to meet your retirement needs. Assume the valuation rate of 7%.

Part A: If you want to keep a constant level of consumption during your retirement, how much you can consume per year when you are retired? Part B: Imagine you decide to save 20% of your salary. How many years earlier you can retire having the same level of consumption as Part A during your retirement? Hint: (1+)⁹⁰=(1+)²⁰ /(1+)⁷⁰=(1+) /(1+)⁹⁰

^{PLEASE SHOW ALL THE WORKINGS}