Interest rate swap problem

**downthesun01** · June 5th 2012, 03:35 AM

An interest rate swap is based on the yield curve given below.

$s_{1}=0.03$
$s_{2}=0.04$
$s_{3}= x$
$s_{4}=0.05$

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.

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

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

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

From there

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

Which isn't correct. The book shows

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

Can someone point my mistake out please? Thanks

**Wilmer** · June 7th 2012, 01:18 AM

You should use use .04936 as swap rate (kick yourself!).

Also, your 2.77725.... is not quite right: I get 2.71813...

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