18.2 eleanor needs $40,000 a year to live on in retirement net of the
In order to calculate the lump sum that Eleanor needs at the beginning of her retirement period, we first need to adjust for inflation. According to the 3.5% expected annual inflation rate, $40,000 in 22 years will be equivalent to $90,050.81 in today’s dollars.
Next, we must determine how much money she will need each year after taxes have been taken out – given an expected after-tax return on investments of 5%, this comes out to be approximately $83,413.60 per annum (with a total over 25 years of $2,085,340). Finally then, we can use these figures to calculate the lump sum needed at the start of her retirement:
Lump Sum Needed = ($90,050.81 * 25 years) / (1+0.05^25) = $2,335,368