Respuesta :
Answer:
[tex]V_{I}=-11812.39[/tex]
[tex]V_{R}=-810.81[/tex]
Explanation:
We will first state the equation.
[tex]V(I,R)=1000[\frac{1+0.07(1-R)}{1+I}]^{10}[/tex]
Where:
I = annual rate of inflation;
R = the tax rate for the person making the investment.
We first determine the partial derivatives with respect to I and R.
[tex]\frac{dV}{dI}=-10000\frac{(1+0.07(1-R))^{10}}{(1+I)^{11}}[/tex]
[tex]\frac{dV}{dR}=-700\frac{(1+0.07(1-R))^{9}}{(1+I)^{10}}[/tex]
VI(0.03, 0.28)
[tex]\frac{dV(0.03,0.28}{dI}=-10000\frac{(1+0.07(1-0.28))^{10}}{(1+0.03)^{11}}[/tex]
=-11812.39
[tex]\frac{dV(0.03,0.28)}{dR}=-700\frac{(1+0.07(1-0.28))^{9}}{(1+0.03)^{10}}[/tex]
=-810.81
