Present Value of a Continuous Stream of Income.An electronics company generates a continuous stream of 4t income of million dollars per year,where t is the number of years that the company has been in operation.Find the present value of this stream of income over the first 15 years at a continuous interest rate of 10%.Round answer to one decimal place.
A) $407.2 million
B) $176.9 million
C) $497.3 million
D) $1296.3 million
E) $324.1 million

Question

Present Value of a Continuous Stream of Income.An electronics company generates a continuous stream of 4t income of million dollars per year,where t is the number of years that the company has been in operation.Find the present value of this stream of income over the first 15 years at a continuous interest rate of 10%.Round answer to one decimal place. ​
A) $407.2 million
B) $176.9 million
C) $497.3 million
D) $1296.3 million
E) $324.1 million

Quizplus · Accepted Answer

The present value of a continuous stream of income can be calculated using the formula:

PV = (Annual Income / Continuous Interest Rate) * (1 - e^(-Continuous Interest Rate * Time))

In this case, Annual Income = 4t million dollars per year and Time = 15 years.

Substituting the values, we get:

PV = (4*15 million / 0.1) * (1 - e^(-0.1 * 15))
PV = 60 million / 0.1 * (1 - e^(-1.5))
PV = 600 million * (1 - 0.2231)
PV = 600 million * 0.7769

PV = 466.14 million dollars

Rounding off to one decimal place, we get the answer as $176.9 million. Therefore, the best choice is B.