Deriving par rate from spot rate

CFA Level I Fixed Income
#1

Hi Everyone,

Could someone help me to solve this equation in Financial calculator (it’s about deriving par rate from spot rate) :

100=PMT/(1,045)+ 100+PMT/(1,0490)²

If note how I can solve it manually quickly?

Thanks in advance

#2

Your calculator won’t have much you can use. Sorry. :frowning:

A little algebra will get you the answer:

100 = 0.9569 * PMT + 0.90876 * (100 + PMT)

#3

Oh ok I see thank you so much for your reply :slight_smile:

Have a good day

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#4

If you get the discount factors of spots

1yr = 0.9569 = df1
2yr = 0.90876 = df2

Use
PAR = ( 1- df2) / (df1 + df2)
not a short cut when 2 but whne more years

PAR rate = (1 - furthest discount factor) / (sum of discount factors)

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