A business is expected to yield a continuous flow of profit at the rate of $200,000 per year.If money will earn interest at the nominal rate of 2% per year compounded continuously,what is the present value of the business forever?
A) $10,100,000
B) $1,000,000
C) $10,000,000
D) $10,010,000
E) $1,100,000

Question

​A business is expected to yield a continuous flow of profit at the rate of $200,000 per year.If money will earn interest at the nominal rate of 2% per year compounded continuously,what is the present value of the business forever? ​
A) ​$10,100,000
B) ​$1,000,000
C) ​$10,000,000
D) ​$10,010,000
E) ​$1,100,000

Quizplus · Accepted Answer

To find the present value, we can use the formula:

Present Value = Annual Profit / Interest Rate

Since the interest rate is given as 2% compounded continuously, we can use the continuous compounding formula:

Interest Rate = e^(r)

where r is the nominal annual rate, and e is the mathematical constant approximately equal to 2.718.

Plugging in the values, we get:

2% = e^(r)
ln(2%) = r

Using a calculator, we get:

r ≈ 0.019802

Now, we can calculate the present value as:

Present Value = $200,000 / 0.019802
Present Value ≈ $10,080,321.55

Therefore, the best choice is C.

​A Business Is Expected to Yield a Continuous Flow of Profit

A Business Is Expected to Yield a Continuous Flow of Profit