Question

You are offered and investment opportunity that will produce continuous income at a constant rate of 8000 dollars/year for 15 years. if the annual interest rate is 7%, continuously compounded, what is the present value of this income stream?

Answer 1

The present value of the continuous income stream is approximately $81,327.70.

Step-by-step explanation:

To calculate the present value of the income stream, we can use the formula for the present value of a continuous income stream:

PV = (CF / r) * (1 - e^(-rt))

Where PV is the present value, CF is the cash flow per year, r is the interest rate, and t is the time period. Plugging in the given values, we have:

PV = (8000 / 0.07) * (1 - e^(-0.07 * 15))

Calculating this expression gives us a present value of approximately $81,327.70