Question

The value of an investment of $1000 earning 5% compounded annually is V(I, R) = 1000 1 + 0.05(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.

a. Calculate VI(0.03, 0.28) and VR(0.03, 0.28).

b. Determine whether the tax rate or the rate of inflation is the greater "negative" factor in the growth of the investment.


i. The rate of inflation has the greater negative influence.

ii. The tax rate has the greater negative influence

Answer 1

VI = -10,289.4

VR = -511.485

The inflation rate is the greater negative factor

The inflation has the greater negative influence.

Explanation:

Given

V(i, R) =1000[1 +0.05(1-R)]^10 (1+I)^-10

We need to find

dV/di = VI = inflation rate

dV/dr = VR = tax rate

VI = -10,289.4

VR= -511.485

VI > VR

Hence VI has the greater negative factor and It therefore has the greater negative influence.

See attachment for differentials.