Charlene plans to place an annual savings amount of A = $27,185 into a retirement program at the end of each year for 20 years starting next year. She expects to retire and start to draw a total of R = $60,000 per year 1 year after the 20th deposit. Assume an effective earning rate of i = 6% per year on the retirement investments and an infinite life. Determine and comment on the sensitivity of the size of the annual withdrawal R for variations in A and i. Show hand and spreadsheet solutions.

(a) Variation of ± 5% in the annual deposit A.

(b) Variation of ± 1% in the effective earning rate i, that is, ranging from 5% to 7% per year.