Today (year 0) you are planning for retirement. You plan to save for the next 25 years, making deposits of $20,000 into a savings account at the end of every year beginning next year and ending in 25 years (years 1,2,…,25). After that, the balance of your savings will remain invested for 4 more years without any additional deposits or withdrawals (until year 29). You will make withdrawals of the equal sum at the end of every year for the following 15 years (retirement period). The first withdrawal will be 30 years from now and the last withdrawal will be 44 years from now. After your last withdrawal, you plan that your account will have a balance of $250,000. The (nominal) interest rate is 4percent. Ignore taxes and inflation (for now).
(i) What would be the value of your savings account after 25 years?
(ii) How much does this plan allow you to withdraw every year during your retirement period?
(iii) Now assume that instead of the above withdrawals, you want to make equal withdrawals in today’s dollars (i.e., equal in real terms). Also, assume that you want to have $250,000 in today’s dollars after your last withdrawal. The inflation rate is 1.9% per year throughout the entire period. What amount (in today’s dollars i.e., in real terms) will you be able to withdraw in each of the 15 years?
(iv) Using the same data from (iii) what are the actual (nominal $) withdrawal amounts for your first and second year of retirement?