MONEY MARKET INTEREST RATES
Equation 1.8, which allows the conversion of a discount rate to an add-on rate when both are quoted for the same day-count convention, is derived by assuming that the cash flows, PV and PV, are the same for each rate quotation. To derive the equation, first rewrite equations 1.3 and 1.6.
Equate these two expressions.
Subtract 1 from each side.
Simplify the numerator on the right side.
Multiply each side of the equation by Year/Days.
Multiply the numerator and denominator by Year to get equation 1.8.
Equation 1.11 is the official Investment Rate conversion formula for Treasury bill discount rates having six months or less to maturity. It converts the 360-day discount rate to a 365-day add-on basis. The equation can be derived by letting IR = AOR and Year = 365 in A1.1 and Year = 360 in A1.2.
Combine the equations.