Skip to content
Interview prep / Finance/Derivatives

Implied forward rate between years five and ten

Question

The five-year spot rate is 10%10\% and the ten-year spot rate is 15%15\%. What forward rate applies from year five to year ten?

Short answer

About 20%20\%. With continuous compounding, f=15%×10−10%×55=20%f = \frac{15\% \times 10 - 10\% \times 5}{5} = 20\%. With annual compounding, (1.1510/1.105)1/5−1≈20.2%(1.15^{10}/1.10^5)^{1/5} - 1 \approx 20.2\%. Either way, investing ten years at 15%15\% must match five years at 10%10\% followed by five at ff.

Adapted from Crack, Heard on the Street, Q3.3, p.33; question and answer rewritten by SelfMadeQuant.com.

See the hint and the full worked solution in the question bank (free account).

Open the worked solution

Lessons behind this question

Start with a free lesson: Forwards and Futures is part of a free topic. Create a free account, no card needed, to read it in full with worked solutions.

Read it free