It might be a bit daft but I find these two formulas very similar but they give very different answers

In formula 1, *r* is an effective (annual) interest rate; i.e., it takes compounding into account.

In formula 2, *r* is a nominal (annual) interest rate; i.e., it does not take compounding into account.

thank you for your reply

but for calculation of effective annual int rates we have to divide r by the no. of compounding periods like for semi annual it would be (1 + r/2)^2 but for calculating the forward price F0(T) = S0 (1 + r)^ 6/12

but for FRA we use [NA x( mrr x period/360)] I am having difficulty wrapping my head around this

Edit : just one more thing what is assumed to be the compounding frequency on the effective annual rate?

To add to the magician’s excellent answer

(1) is (1+r)^t and (2) is 1+rt, where t is the time in years.

(1) is continuously compounded.

but for calculation of effective annual int rates we have to divide r by the

no. of compounding periods like for semi annual it would be (1 + r/2)^2

If you have 1 payment during the period, at the end of the period you have 1+rt

If you have 2 payments during the period, at the end of the period you have (1+rt/2)^2

If you have 3 payments during the period, at the end of the period you have (1+rt/3)^3

If you have n payments during the period, at the end of the period you have (1+rt/n)^n

If you let n get really big (take the limit as n\to\infty), you have continuous compounding and

\lim_{n\to\infty}(1+rt/n)^n=e^{rt}.

How is this related to (1)?

(1) was (1+r)^t which you can write as e^{t\log(1+r)}

thank you for your answer

ah now I see, would I be correct to assume formula (2) as sort of a holding period return

And also If I want to calculate the future value of an amount given r = 5% compounded annually after 6 months I would apply the following formula FV= PV (1 + .05)^6/12

thanks once again for your answer!

Edit I’m trying my best to not be annoying but the rate used while calculating Forwards price is the interbank rate which is compounded continuously which make using (1 + r)^period/360 correct but is this also applicable to formulas where r is an annually compounded rate

e^{t\ ln\left(1+r\right)}