Pretty simple question but I’m simply stuck on calculating a swap curve from spot rates. I know the answer is simple but I’m at my wits end.

I’m using CFAI L2 material at the moment, volume 5 page 28. The example is creating a swap curve from spot rates.

Given a spot rate for year 1 (5%) and year 2 (6%) the formula to solve is as follows

(SFR2/1.05) + (SFR2/(1.06)^{2}) + 1/(1.06)^{2} = 1

I get to through the 1st step and end up with (SFR2/1.05) + (SFR2/(1.06)^{2}) = 0.110004

But, it’s here that no matter how I think I should solve it, I can’t figure out what i’m doing wrong. Multiplying both sides of the equation by (1.06)^{2} and then doing the same with 1.05 ends up with values that are higher than the actual result of 5.97%

When someone has a moment, would you walk me through the algebra related to this? I have a big blind spot here.

Thanks.