Answer:
$30,000
Step-by-step explanation:
The capital value is given by
[tex]\int_{0}^{\infty} R(t) e^{-r t} dt[/tex]
where R(t) is annual rate
r - annual rate of interest
capital value [tex]= \int_{0}^{\infty} 1200 e^{0.03t} e^{-0.07 t} dt[/tex]
= lim at b tend to infinity[tex] \int_{0}^{b} 1200 e^{0.03t} dt[/tex]
=lim at b tend to infinity [tex] \left [ \frac{1200}{-0.04} e^{-0.04 t} \right ]_0^b[/tex]
-30,000 { lim at b tend to inifinity[tex] (e^{-0.04 b) = e^0][/tex]
As[tex]b\rightarrow \infty, e^{-0.04 b} \rightarrow 0[/tex]
[tex]\int_{0}^{\infty} 1200 e^{0.03t} e^{-0.07 t} dt = -30,000(0 -1) =$30,000[/tex]
