As for the calculations, let's break them down: 1. High rate (8%): The initial deposit required would be calculated as follows: PV = $1,000,000 / (1+0.08)^40 PV = $1,000,000 / (1.08)^40 PV = $1,000,000 / 21.725 PV = $46,051.13 2. Low rate (4%): With a 4% rate of return, the initial deposit required increases: PV = $1,000,000 / (1+0.04)^40 PV = $1,000,000 / (1.04)^40 PV = $1,000,000 / 4.801 PV = $208,206.91 3. Market average rate (6%): At the average market rate of return, the initial deposit required would be: PV = $1,000,000 / (1+0.06)^40 PV = $1,000,000 / (1.06)^40 PV = $1,000,000 / 10.286 PV = $97,206.77 These calculations can be easily replicated in a spreadsheet using the formula for present value