Today is your 35th birthday and it occurs to you that your current retirement savings may be insufficient to maintain for you the lifestyle to which you have become accustomed. The value of your retirement account today on your 35th birthday is $100,000. You plan to retire on your 65th birthday and to live until the day before your 83rd Your goal is to have a stream of cash payments on your 66th through 82nd birthdays that provides you with $150,000 of consumption annually in terms of today’s purchasing power. Your retirement account earns 10% per year (this is the effective annual rate), and the inflation rate is 2% forever. Ignore the value of your other assets and perform calculations as if deposits, withdrawals, and compounding of interest occur only once a year.
What cash (nominal) balance do you need in your retirement account on your 65th birthday to provide you with your desired retirement spending stream; i.e., what is the PV of all the cash flows at your 65th birthday received between your 66th and 82th birthday?
What constant nominal amount would you have to deposit on each of your 36th through 65th birthdays to ensure that the balance in your account on your 65th birthday is the amount calculated in the previous question? Take into account the $100,000 you already have in your retirement account.