Assume you are now $21$ years old and will start working as soon as you graduate from college. You plan to start saving for your retirement on your $25$th birthday and retire on your $65$th birthday. After retirement, you expect to live at least until you are $85.$ You wish to be able to withdraw $$60,000($in today$$s dollars$)$ every year from the time of your retirement until you are $85$ years old $($i$.$e$.,$ for $20$ years$).$ The average inflation rate is likely to be $5$ percent.

Calculate lump sum you need to have accumulated at age $65$ to be able to draw the desired income. Assume the annual return on your investments is likely to be $10\%$

b$.$ What is the dollar amount you need to invest every year, starting at age $26$ and ending at age $65($i$.$e$.,$ for $40$ years, to reach the target lump sum at age $65?$

c$.$ Now answer questions a$.$ and b$.$ assuming the rate of return to be $8$ percent per year, then again at $15$ percent per year.

d$.$ Now assume you start investing for your retirement when you turn $30$ years old and analyze the situation under rate of return assumptions of $($i$)8$ percent, $($ii$)10$ percent, and $($iii$)15$ percent.

e$.$ Repeat the analysis by assuming that you start investing only when you are $35$ years old