Question

Capital Value An investment produces a perpetual stream of income with a flow rate of

Answer 1

Answer:

$30,000

Step-by-step explanation:

The capital value is given by

$\int_{0}^{\infty} R(t) e^{-r t} dt$

where R(t) is annual rate

r - annual rate of interest

capital value $= \int_{0}^{\infty} 1200 e^{0.03t} e^{-0.07 t} dt$

                      = lim at b tend to infinity$\int_{0}^{b} 1200 e^{0.03t} dt$

                      =lim at b tend to infinity $\left [ \frac{1200}{-0.04} e^{-0.04 t} \right ]_0^b$

-30,000 { lim at b tend to inifinity$(e^{-0.04 b) = e^0]$

As$b\rightarrow \infty, e^{-0.04 b} \rightarrow 0$

$\int_{0}^{\infty} 1200 e^{0.03t} e^{-0.07 t} dt = -30,000(0 -1) = 30,000$