You are 35 years old today and are considering your retirement needs. You expect to retire at age 65 and your actuarial tables suggest that you will live until 100. Your living expenses in retirement will be $ 30,000 a year (starting at age 66 until 100). r=8%.

a. How much will you need to have saved by your retirement date to afford that? Give formula (in age 65 dollars).

b. Assume you already have $ 50,000 in retirement savings. If you can invest the money at 8% per year, how much would you need to save each year for the next 30 years to be able to afford this retirement plan?

c. What portion of your retirement wealth will you have saved by age 50? Give formula.

d. Imagine at age 50, interest rate unexpectedly and permanently drops from 8% to 4%. Everything else in the question stays constant (i.e., you still wish to spend $30K per year in retirement). Does the change make you better off or worse off? Explain briefly.