The margin of safety is the excess of budgeted or actual sales dollars over the break-even volume of sales dollars. it is the amount by which sales can drop before losses are incurred. the higher the margin of safety, the lower the risk of not breaking even and incurring a loss. the formula for the margin of safety is:

You wish to retire in 13 years, at which time you want to have accumulated enough money to receive an annual annuity of $23,000 for 18 years after retirement. during the period before retirement you can earn 9 percent annually, while after retirement you can earn 11 percent on your money. what annual contributions to the retirement fund will allow you to receive the $23,000 annuity? use appendix c and appendix d for an approximate answer, but calculate your final answer using the formula and financial calculator methods.