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Maslowich
3 years ago
8

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

Mathematics
1 answer:
Elodia [21]3 years ago
6 0

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]

Asb\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

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