I am currently reading Chapter 3 of Tuckman's 'Fixed Income Securities' and it states that we can write the price of a bond using its term structure in terms of forward rates but with periods of unspecified length as follows:
$P = \frac{c}{1+f(1)}$$+\frac{c}{(1+f(1))(1+f(2))}$+...+$\frac{1+c}{1+f(1))(1+f(2))...(1+f(T))}$, where $c$ is the coupon and $f(1),f(2)...$ equal forward rates.
But I am not sure how the 'periods of unspecified length' reconcile with the equation above - from what I know, where f(t) = the forward rate from year t-0.5 to year t and assuming semiannual compounding:
$P = \frac{c}{2}[\frac{1}{1+\frac{f(0.5)}{2}}+\frac{1}{(1+\frac{f(0.5)}{2})(1+\frac{f(1)}{2})}+...+\frac{1}{(1+\frac{f(0.5)}{2})(1+\frac{f(1)}{2})...(1+\frac{f(T)}{2})}]+\frac{1}{(1+\frac{f(0.5)}{2})(1+\frac{f(1)}{2})...({1+\frac{f(T)}{2}})}$.
Answers would be very much appreciated!