finance perpetuity question

Question

Anne plans to retire at 65 and wants a perpetual monthly income of $4000 from then on. Knowing that market fluctuations happen, she invested in a fund that pays the Inflation Index + 6% per year to guarantee she won’t lose money with the devaluation of the currency in relation to inflation.

Anne calculates how much the 6% coupon is equivalent to monthly and applies the perpetuity formula, thus obtaining an estimate for the amount she needs to have saved to reach her goal. This amount will be approximate:

a) 1 million

b) 900 thousand

c) 820 thousand

d) 740 thousand

Answer 1

6%/yr is 0.06/12 = 0.005 of 0.5%/mo.

To earn interest of $4,000/mo you need to have a balance of 4000/0.005, or $800,000. That way the withdrawal is offset by an equal amount of interest earned and the balance is untouched.

On an annual basis: $4,000/mo = $48,000/yr. At 6% annual interest, 48000/0.06 = $800,000 required (same result).

If you can, see Example 4 re: A Comfortable Retirement. Ch 4C pg 221 "Using and Understanding Mathematics, A Quantitative Reasoning Approach" (Bennett and Briggs) Pearson Addison Wesley 5th Edition 2011.