Question

Andrew receives $300,000 as a lump sum at age 65. His account earns interest at 5% per annum, and he expects his cost of living to increase by 2% p.a. compound.

He intends to withdraw $C at the end of the first year, and then $C*(1.02) at the end of the second year, C*(1.02)^2 at the end of the third year, and so on, each year for the next 30 years (after that time, if he is still alive, he intends to rely on the old age pension provided by the government). What is the value of $C which will result in a zero balance after 30 years?

Answer 1

To find the initial withdrawal value C that results in a zero balance after 30 years, an equation must be set up to equate the present value of the increasing withdrawals to the initial sum of $300,000. This equation can be solved using financial tools or software.

Step-by-step explanation:

The question involves finding the value of an annuity C that increases at a compound rate of 2% per annum such that a lump sum of $300,000 will be depleted exactly after 30 years with an account earning 5% per annum interest. To solve this problem, we need to set up an equation that equals the present value of the withdrawals (which are a growing annuity) to the lump sum of $300,000. This equation is a bit complex but can be solved using financial calculators or spreadsheet software. The withdrawals are structured so that the first withdrawal is C, the second year withdrawal is C*(1.02), the third year is C*(1.02)^2, and so on for 30 years. By establishing this equation and solving for C, we can determine the initial withdrawal amount that allows the balance to reach zero after 30 years, taking into account the 5% interest earned annually and the 2% annual increase in withdrawals.