Answer
$\approx\$ 333,333.33$
Work Step by Step
The present value of the income stream after $T$ years can be computed as:
$\int_0^T (10,000e^{0.01t})e^{-0.04t} dt=[\dfrac{10,000e^{0.03t}}{-0.03}]_0^T\\=333,333.33(1-e^{-0.03T}) $
Now, the present value of the entire income stream will be:
$\int_0^{\infty} 10,000e^{-0.03t} dt=\lim\limits_{T \to \infty}\int_0^T 10,000e^{-0.03t} \ dt \\=\lim\limits_{T \to \infty} 333,3333.33 (1-e^{-0.03T} \\ \approx\$ 333,333.33$
