On Margarets 30th birthday, she gets a good job and starts to think about saving for her ideal retirement in the Bahamas. She expects to retire at age 70 after working for 40 years and to live for another 30 years in retirement. At todays price level, she decides that an income of $150,000 per year before taxes would provide for a comfortable retirement. Although she currently has no retirement savings, she expects that she can earn an annual real rate of return of 9% on her retirement savings while she is working. However, when she retires she will invest in safer assets that will produce an annual real rate of return of only 3% per year (assume annual compounding). Current expectations are that the inflation rate will average 2% per year into the future. a. Determine the size of investment nest egg at todays prices (removing effects of inflation) she will need to have accumulated at retirement (40 years from now) in order to finance her retirement annuity of $140,000 / year (at todays prices) for 3 years of retirement. Assume that in retirement you need an immediate annuity (i.e., first real CF at todays prices of $140,000 comes out at time zero of the retirement period). b. What will the dollar balance of this nest egg in part (a) actually need to be in actual future dollars in 40 years when Margaret retires (including the expected inflation)? c. Determine the constant amount in real terms (dollars at todays prices) she needs to put away each year (at the end of the year) starting one year from today in order to achieve the nest egg determined in part a by the beginning of her retirement (end of your 40th year of saving.)