How to convert between a bank discount yield and a money market yield

The bond books describe the bank discount yield as $(F-P)/F \times 360/D$ and the money market equivalent yield as $(F-P)/PP \times 360/D$.  Let's combine these two equations.  Why?  in doing so, we will arrive at a relationship between the discount yield $y_d$ and the money market equivalent yield $y_m$.  This means you can do a direct yield to yield translation if required.

It turns out that $y_m = \frac{F}{P}y_d$.  Usually $F > P$ so $y_m > y_d$ so the discount yield will always look artificially lower than the money market convention, so you're up scaling the yield in the move from discount to money market.

Also, plugging this newly found relation back into original pair of equations, you see that $y_m = y_d \times \frac{360}{360 - D \times y_d}$ where $D$ is the number of days in the holding period. Again the numerator is greater than the denominator.