Question

Sam and Sally are both 30 years old, and beginning in exactly 1 year they will save $24,000 per year for 30 consecutive years to support their retirement. When they reach retirement at age 60, they will begin to withdrawal an annuity amount per year to enjoy their retirement years. The withdrawals will start in one year, and continue for 25 consecutive years. What is the maximum amount they can withdrawal if interest rates are 3%?

Answer 1

To start with, we will first need to calculate the total amount of money that Sam and Sally can save up until their retirement starting from year 1 of saving till year 30. The key point to keep in mind here is that the interest earned will compounded year on year i.e. the interest earned in Year 1, will itself earn interest in year two. Therefore the easiest way to calculate the saving at the end of 30 years is to construct a table as below. The assumption here is that the saving of $24,000 happens at the end of each year.

The closing balance in each year is the sum of the Opening balance for the year, the investment in the year and the interest earned during the year. The interest in any particular year will be earned on the opening balance for that year, since it is assumed that the saving happens at the end of the year. In excel, this can be achieved by using the formula for future value i.e. FV(3%,30,24000) = $1,141,810

To understand how much is the maximum amount Sam and Sally can withdraw annually, we use the brute force method of calculation. From the above table, at the end of 30 years, Sam and Sally have $1,141,810 as savings. From this amount, a certain amount will be withdrawn at the beginning of each year and the remaining amount will continue to earn interest at 3%. Therefore, closing balance for a particular year will be opening balance minus withdrawals plus interest earned, where interest earned will be 3% of opening balance minus withdrawals.

From the above table, Sam and Sally can withdraw upto $63,661.86 per year for the next 25 years to exhaust their entire corpus in 25 years.

The key assumption in this exercise is that the saving is done at the end of the year and the withdrawal is done at the beginning of the year.