Julie is ready to retire. She wants to receive the equivalent of $40,000 in todays dollars at the beginning of each year for the next 25 years. She assumes inflation will average 3%, and she can earn a 10% after-tax return (compounded annually) on her investments. What lump sum does she need to invest today to attain her goal?

Diane and Andy are ready to retire. They want to receive the equivalent of $75,000 in todays dollars at the beginning of each year for the next 30 years. They assume inflation will average 3.5% over the long run, and they can earn a 9% after-tax return (compounded annually) on their investments. What lump sum do they need to invest today to attain their goal?