An interest rate swap is based on the yield curve given below.$\displaystyle s_{1}=0.03$

$\displaystyle s_{2}=0.04$

$\displaystyle s_{3}= x $

$\displaystyle s_{4}=0.05$

The fixed payment swap rate is R=0.4936. Find the 3-year spot rate x.I'm having trouble solving for x. For some reason I keep getting a negative number. This is what I've been doing.

$\displaystyle R=0.4936=\frac{1-\frac{1}{1.05^{4}}}{\frac{1}{1.03}+\frac{1}{1.04^{ 2}}+\frac{1}{(1+x)^{3}}+\frac{1}{1.05^4}}$

$\displaystyle => \frac{0.177297525}{2.7772586888+\frac{1}{(1+x)^{3} }}=0.4936$

$\displaystyle 0.177297525=0.492401092+\frac{0.4936}{(1+x)^{3}}$

From there

$\displaystyle \frac{1}{(1+x)^{3}}=-2.418065972$

Which isn't correct. The book shows

$\displaystyle \frac{1}{(1+x)^{3}}=0.87379$

Can someone point my mistake out please? Thanks