Q4.2 Estimate the amount of cash you will need each year over the next 20 years to live at the standard you desire. Also estimate the rate of return you can reasonably expect to earn annually, on average, during that 20-year period by investing in a common stock portfolio similar to the S&P 500.

a. How large a single lump sum would you need today to provide the annual cash required to allow you to live at the desired standard over the next 20 years? (Hint: Be sure to use the appropriate discount rate.)

b. Would the lump sum calculated in part a be larger or smaller if you could earn a higher return during the 20-year period? Explain.

c. If you had the lump sum calculated in part a but decided to delay your planned retire- ment in 20 years for another three years, how much extra cash would you have accumu- lated over the three-year period if you could invest it to earn a 7% annual rate of return?