Calculate par curve from spot curve

I know how to bootstrap the par curve to get the spot curve. But I’m trying to figure out how to go the other way and get the par curve from the spot curve.

1 year spot rate = 1.0%

2 year spot rate = 1.201%

3 year spot rate = 1.251%

1 year par rate = 1.0%

2 year par rate = ?

3 year par rate = ?

Let x = 2 year par rate

100 = (x/1.01) + [(100+x)/1.012012]

Is there a faster way than solving for x?


(Note that in your formula, x isn’t the par rate; it’s the par _ coupon payment _ on a principal of 100. You need to divide it by 100 to get the par rate. If you replaced your two 100s with 1s, then x would be the par rate.)