Annual effective discount rate
The annual effective discount rate expresses the amount of interest paid or earned as a "percentage" of the balance at the "end" of the annual period. It is related to but slightly smaller than the effective rate of interest, which expresses the amount of interest as a "percentage" of the balance at the "start" of the period. The discount rate is commonly used for U.S. Treasury bills and similar financial instruments. For example, consider a government bond that sells for $95 ('balance' in the bond at the start of period) and pays $100 ('balance ' in the bond at the end of period) in a year's time. The discount rate is The effective interest rate is calculated using 95 as the base which says that formula_3 of $105.26 is $100. For every effective interest rate formula_4, there is a corresponding effective discount rate formula_5 that can produce the same future value as formula_4 if a given amount of principal is invested for the same amount of time at each of the rates formula_4 and formula_5, and they are said to be "equivalent". Therefore, we have the following relationship between two equivalent rates  formula_4 and formula_5. Using this, we can derive the following expression of formula_5 and formula_4. We usually define formula_16 as the discount factor which is given by using the above relationships between formula_4 and formula_5. Annual discount rate convertible thly. A discount rate applied formula_22 times over equal subintervals of a year is found from the annual effective rate d as where formula_24 is called the annual nominal rate of discount convertible formula_22thly. formula_27 is the force of interest. The rate formula_24 is always bigger than d because the rate of discount convertible formula_22thly is applied in each subinterval to  a smaller (already discounted) sum of money. As such, in order to achieve the same total amount of discounting the rate has to be slightly more than 1/pth of the annual rate of discount. Business calculations. Businesses consider this discount rate when deciding whether to invest profits to buy equipment or whether to deliver the profit to shareholders. In an ideal world, they would buy a piece of equipment if shareholders would get a bigger profit later. The amount of extra profit a shareholder requires to prefer that the company buy the equipment rather than giving them the profit  now is based on the shareholder's discount rate. A common way of estimating shareholders' discount rates uses share price data is known as the capital asset pricing model. Businesses normally apply this discount rate by calculating the net present value of the decision. References. https://web.archive.org/web/20131230232348/http://www.mcu.edu.tw/department/management/stat/ch_web/etea/Theory%20of%20Interest/interest2.pdf