Independent solution

How to solve this Spot Rate from Forward Rates question

Setup

Setup

The first three one-year forward rates are 4%, 6%, and 8%. A three-year zero-coupon accumulation must equal the product of these three annual forward accumulations.

s1=0.04,(1+s2)2=(1.04)(1.06)s_1=0.04,\quad(1+s_2)^2=(1.04)(1.06)

Model

Model

Thus (1 + s₃)³ = 1.04 × 1.06 × 1.08. This no-arbitrage product, not an arithmetic average of rates, determines the spot rate.

(1+s3)3=(1+s2)2(1.08)(1+s_3)^3=(1+s_2)^2(1.08)

Compute

Compute

Taking the cube root gives s₃ = 0.05987, which rounds to 6%.

s3=[1.04(1.06)(1.08)]1/3−1=0.05987s_3=[1.04(1.06)(1.08)]^{1/3}-1=0.05987

Answer

Answer

The calculation gives 6% for spot rate from forward rates, matching published choice C.

s3=6%(C)\boxed{s_3=6\%\quad\text{(C)}}