Show that the swap rate for a standard swap with level notional amount is the same as the at-par yield rate for a bond with same t

Question

Show that the swap rate for a standard swap with level notional amount is the same as the at-par yield rate for a bond with same time to maturity as the length of the swap. At-par yield was defined in Chapter 6 as coupon rate r at which a bond would have a yield to maturity of r under the current term structure.

Rylee · Answer

Step-by-step explanation:         orange{ bold{ underbrace{ overbrace{❥Question᎓}}}}     Integrate the function      huge green tt frac{  sqrt{tanx} }{sinxcosx}}     ⇛  huge tt frac{  sqrt{tanx} }{sinxcosx}   ㅤ ㅤ ㅤ ㅤ ㅤ    ⇛  huge tt  frac{  sqrt{tanx} }{sinxcosx  times  frac{cosx}{cosx}}      ㅤ ㅤ ㅤ ㅤ ㅤ    ⇛  huge tt  frac{  sqrt{tanx} }{sinx  times  frac{ {cos}^{2} x}{cosx}}  ㅤ ㅤ ㅤ    ⇛   huge tt frac{  sqrt{tanx} }{ {cos}^{2} x  times  frac{sinx}{cosx} }   ㅤ ㅤ ㅤ ㅤ ㅤ    ⇛  huge tt frac{  sqrt{tanx} }{ {cos}^{2}x  times tanx }   ⇛  huge tt {tan}^{  frac{1}{2} - 1 }  times  frac{1}{ {cos}^{2} x} ㅤ ㅤ ㅤ ㅤ ㅤ    ⇛  huge tt {(tan)}^{ -  frac{ 1}{2} }  times  frac{1}{ {cos}^{2}x } = {(tanx)}^{ -  frac{1}{2} }  times {sec}^{2} x⇛(tan)   ㅤ ㅤ ㅤ ㅤ ㅤ    ⇛  huge tt {(tan)}^{ -  frac{ 1}{2} }  times  frac{1}{ {cos}^{2}x } = ∫ {(tanx)}^{ -  frac{1}{2} }  times {sec}^{2} x  times dx⇛(tan)   ㅤ ㅤ ㅤ ㅤ ㅤ      bold blue{☛ : Let tanx=t}     bold blue{☛  :Differentiating  : both  : sides  : w.r.t.x}   ㅤ ㅤ ㅤ ㅤ ㅤ    ⇛  huge tt {sec}^{2} x =  frac{dt}{dx}     ⇛  huge tt{dx  frac{dt}{ {sec}^{2}x }}     ㅤ ㅤ ㅤ ㅤ ㅤ    ⇛  huge tt∴∫ {(tanx)}^{ -  frac{1}{2} }  times {sec}^{2} x  times dx     ⇛  huge tt ∫ {(t)}^{ -  frac{1}{2} }  times {sec}^{2} x  times  frac{dt}{ {sec}^{2}x }     ⇛  huge tt ∫ {t}^{ -  frac{1}{2} } ㅤ ㅤ    ⇛   huge tt frac{ {t}^{ -  frac{1}{2} + 1} }{ -  frac{1}{2} + 1 }     ⇛   huge tt  frac{ {t}^{  frac{1}{2} } }{  frac{1}{2} } + c = 2 {t}^{  frac{1}{2} } + c = 2  sqrt{t}     ⇛  huge2  sqrt{t} + c = 2  sqrt{tanx}     ╚════════════════════════

Alice · Answer

Answer:   I  don't understand    Step-by-step explanation:   but please mark me as a brainlist

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