I struggled this forward rate agreements this weekend myself. I simplify by remembering to put the entire term in the numerator (h + m), unannualizing it, and then singling out the unannualized term I’m ‘betting on’ by dividing by the contract term (h). Then I annualize the whole thing by multiplying by 360/m.
I’m still working on remembering how to value the FRA prior to expiration.