My question pertains to the rates being used in the following examples. In general, To determine the future price of a security (assuming no interim cash flows), we calculate: Spot*(1+RFR)^(days/365). To determine the rate on a 1X3 FRA where 30d Libor is 2.5% and 90d Libor is 3.0%, we calculate: { [[1 + 0.025(90/360)] / [1 + 0.3(30/360)] ] - 1 } (360/60) To determine the one year future value of the coupons of an 8% semi-annual pay bond with par value $1 that expires in one year, we calculate: 0.04(1 + RFR/2) + 0.04. I’m confused as to when to apply exponents and when to apply factors for non-annual terms. Can anyone clarify?

LIBOR is an add-on rate , which means the quote itself is for the second type you show. The Discount factors assume simple returns not compound returns. Other rates such as US Treasury or mortgages are quoted compunding terms which makes the first type of rate calculation more appropriate. The third one is seen in Econ more often , but also Lvl I TVM calculations for coupon paying bonds. This one is yet another convention and use it just like you have shown .

If the applicable convention is related to simple (e.g. 2 and 3) versus compounded (e.g. 1) returns then is there an intuition for determining which one should be applied?

FRAs and Interest rate options use simple, everything else uses compounding