term structure of interest rates

[kalpana]

DMT(i)of solved example on pg22
summation why do you add redemption with no of years

hhow do you get negative derivative of solved egon page 30 Pv^5+Qv^10=62418 because derivative formula implies x^n=nx^n-1

quest no 14.5 how do you get (1+y3)^3(1+f3)(1+f4,3)^3=(1+y7)^7
please do help me out

 

[Neetu Verma]

hhow do you get negative derivative of solved egon page 30 Pv^5+Qv^10=62418 because derivative formula implies x^n=nx^n-1

You are right derivative formula implies x^n =nx^n-1
Here we take derivative with respect to i ,in the equestion
-V'(A)=Pv^5+Qv^10
=P(1+i)^-5 +Q(1+i)^-10
=-5P(1+i)^-6+(-10)Q(1+i)^-11
=-5Pv^6-10Qv^11
V'(A) = 5Pv^6+10Qv^11

quest no 14.5 how do you get (1+y3)^3(1+f3)(1+f4,3)^3=(1+y7)^7

(1+f4,3)^3=[1+y(4+3)]^(4+3)/[1+y4]^4
[1+y4]^4*(1+f4,3)^3=[1+y7]^7 ...............(1)
according to
(1+f3,1)=[1+y4]^4/[1+y3]^3
[1+y4]^4=(1+f3,1)*[1+y3]^3
putting this value in equation (1)
(1+f3)*[1+y3]^3*(1+f4,3)^3=[1+y7]^7