Question

You are offered and investment opportunity that will produce continuous income at a constant rate of 1000 dollars/year for 10 years. if the annual interest rate is 6%, continuously compounded, what is the present value of this income stream?

Answer 1

To find the present value of the income stream, we use the formula for continuous compounding: P = A / e^(rt). Plugging in the values, we find that the present value is approximately $548.81.

Step-by-step explanation:

To find the present value of the income stream, we need to use the formula for continuous compounding:

P = A / e^(rt)

Where:
P = present value
A = annual income
e = Euler's number (approximately 2.71828)
r = annual interest rate
t = number of years

Plugging in the values, we get:
P = 1000 / e^((0.06)(10)) = 1000 / e^0.6 = 1000 / 1.82212 ≈ $548.81

Therefore, the present value of this income stream is approximately $548.81.