# Technical Appendix

## 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

*are the same for each rate quotation. To derive the equation, first rewrite equations 1.3 and 1.6.*

**PV,*** *(A1.1)

* *(A1.2)

Equate these two expressions.

* *(A1.3)

Subtract 1 from each side.

* *(A1.4)

Simplify the numerator on the right side.

(A1.5)

Multiply each side of the equation by **Year/Days.**

(A1.6)

Multiply the numerator and denominator by * Year* to get equation 1.8.

(A1.7)

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* =

*and*

**AOR***= 365 in A1.1 and*

**Year***= 360 in A1.2.*

**Year**(A1.8)

(A1.9)

Combine the equations.

(A1.10)