Question

The value of an investment of $1000 earning 7% compounded annually is V(I, R) = 1000 1 + 0.07(1 − R) 1 + I 10 where I is the annual rate of inflation and R is the tax rate for the person making the investment. Calculate VI(0.03, 0.28) and VR(0.03, 0.28). (Round your answers to two decimal places.) VI(0.03, 0.28) = VR(0.03, 0.28) =

Answer 1

Answer:

$V_{I}=-11812.39$

$V_{R}=-810.81$

Explanation:

We will first state the equation.

$V(I,R)=1000[\frac{1+0.07(1-R)}{1+I}]^{10}$

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.

$\frac{dV}{dI}=-10000\frac{(1+0.07(1-R))^{10}}{(1+I)^{11}}$

$\frac{dV}{dR}=-700\frac{(1+0.07(1-R))^{9}}{(1+I)^{10}}$

VI(0.03, 0.28)

$\frac{dV(0.03,0.28}{dI}=-10000\frac{(1+0.07(1-0.28))^{10}}{(1+0.03)^{11}}$

=-11812.39

$\frac{dV(0.03,0.28)}{dR}=-700\frac{(1+0.07(1-0.28))^{9}}{(1+0.03)^{10}}$

=-810.81