Today is Archie's 50th birthday and his retirement account totals $237,000. He plans to retire in 12 years and is confident that his nest egg will earn 8% annually between now and that time. When he retires, Archie wants to purchase a 20-year annuity from the Gold Star Insurance Company. The annuity carries an interest rate of 6% per year. Archie thinks he will need payments of $80,000 per year to sustain his life style. He is concerned that his current nest egg will not be sufficient to purchase an annuity that will pay $80,000 per year and he wonders if he must save additional money over the next 12 years to achieve his goal and he has come to you for help.
a. Does Archie have a shortfall?
b. If he has a shortfall, how much is it?
c. If he has a shortfall how much additional money must Archie save each year for the next 12 years at 8% interest in order to have enough money to purchase an annuity that will produce payments of $80,000 per year for 20 years?