The way I view problems like this is to visualize the future value of $1 at each of those time points. This makes the question intuitive and helps you understand the discounting, rather than relying on formulas.
This is what I did:
3 year spot rate = 4%: So, 3y FV is 1.04^3
5 year spot rate = 5%: So, 5y FV is 1.05^5
4 year forward rate 3 years from today = 6%: So 7y FV is 1.04^3 * 1.06^4
What is the 2 year forward rate 5 years from today?
I actually wanted to ask about this cause I’m quite confused with spot and forward rates but since someone asked something similar might as well continue the thread instead of starting new one… Say the S3 and 4F3 combinations would essentially mean that the Spot rate would last the first 3 years and the forward rate would continue after for the next 4 years?
Frankly, I’m a bit tired of trying to figure this out, so say if a question comes out like this (basing this logic derived S2000magician’s answer), using the given variables form a timeline and let both sides of the equation have the same duration then solve for the unknown?
If instead you used: (S3)^3 x (4F3)^4 = (S5)^5 x (2F5)^2, it wouldn’t be an approximation but actual value already, correct? Ohai’s explanation looks to be the same…