The Smiths had $110,000 in savings at age 51. They had a desired retirement age of 65. They want to fund through age 92. Assume a 4 percent inflation rate and a 5 percent after-tax rate for investment both pre- and postretirement. They have household income of $140,000, which is increasing at the rate of inflation. Their expenditures including taxes are $125,000 a year. They estimate that in retirement they will receive $28,000 a year together in Social Security and Mr. Smith will receive a $12,000-a-year pension, both in today's dollars.Their retirement expenditures would be $90,000 a year in today's dollars.

a) Calculate the lump sum needed at retirement.