Independent solution

How to solve this Forward Rate from Spot Rates question

Setup

Setup

Let s₂ = 5.0% and s₃ = 5.2% be the annual effective spot rates for maturities two and three. The unknown f is the one-year rate earned between those maturities.

s2=0.050,s3=0.052s_2=0.050,\quad s_3=0.052

Model

Model

No-arbitrage requires a three-year spot investment to match a two-year spot investment followed by the one-year forward investment.

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

Compute

Compute

Solving f = 1.052³/1.05² − 1 gives 0.056, so the forward rate is 5.6%.

f=1.0523/1.052−1=0.056f=1.052^3/1.05^2-1=0.056

Answer

Answer

The calculation gives 0.056 for forward rate from spot rates, matching published choice E.

f=5.6%(E)\boxed{f=5.6\%\quad\text{(E)}}