# Question about Swap Rate Curve (fixed income)

LOS 32.f, volume 5, page 25 (fixed income chapter)

In the example, it says the spot rate for maturity 1 is 3.00%, and therefore…

SFR1/(1+S1) + 1/(1+S1) = 1… plug 3% into S1, and…
SFR1 = 3.00%

however, SFR1 actually = 2.83% when you run the calculation

what is going on here? could someone please help me?

Couldn’t find what you mentioned on Page 25 in the official 2020 textbook.

But assuming it’s a swap that is annually-pay, then the SFR1 should be 3%. Not sure how you computed 2.83% (or was it shown 2.83% in the book?).

\frac{SFR_1}{1+S_1} + \frac{1}{1+S_1} = 1

\frac{SFR_1}{1+ 0.03} + \frac{1}{1+0.03} = 1

\frac{SFR_1}{1.03} = 1 - \frac{1}{1.03} = \frac{0.03}{1.03}

SFR_1 = 1.03 \times \frac{0.03}{1.03} = 0.03 = 3\%

Hey @fino_abama, thanks so much for coming to my rescue

You wrote 1-1/1.03 = 0.03/1.03 in line three, which i do not get

1-1/1.03 is the same as 1-0.97087, or 0.02912. when 0.02912/1.03, i got 0.0283 or 2.83%

am i doing something wrong?

nevermind, i was being an idiot

1 - \frac{1}{1.03} = \frac{1.03}{1.03} - \frac{1}{1.03} = \frac{1.03-1}{1.03} = \frac{0.03}{1.03}

Seems the error is coming from how you solve algebraic equations.

1 - \frac{1}{1.03} = 1 - 0.97087 = 0.02913

Then:

\frac{SFR_1}{1.03} = 0.02913

SFR_1 = 1.03 \times 0.02913

SFR_1 = 0.0300039 \approx 3\%

thank you very much

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When I run the calculation, I get 3%:

z_1 = \frac{1}{1.03} = 0.970873786
SFR = \frac{1 - z_1}{z_1} = \frac{1 - 0.970873786}{0.970873786} = \frac{0.029126214}{0.970873786} = 0.03 = 3\%

yes, you are right. i was just being stupid

We’ve all been there at one time or another.