Independent solution

How to solve this Forward Rate from Spot Curve question

Setup

Setup

Let s₄ = 9.0% and s₅ = 9.5% be the four- and five-year spot rates. The unknown one-year forward rate applies only during year 5.

(1+s5)5=(1+s4)4(1+f4)(1+s_5)^5=(1+s_4)^4(1+f_4)

Model

Model

Equate the five-year spot accumulation with four years at s₄ followed by one year at the forward rate.

s5=0.095,s4=0.090s_5=0.095,\quad s_4=0.090

Compute

Compute

Solving 1 + f = 1.095⁵/1.09⁴ gives f = 0.115, or 11.5%.

f4=1.0955/1.094−1=0.115f_4=1.095^5/1.09^4-1=0.115

Answer

Answer

The calculation gives 11.5% for forward rate from spot curve, matching published choice C.

f=11.5%(C)\boxed{f=11.5\%\quad\text{(C)}}