Question

You are starting an internet business and decide to use the continues flow of funds method for determining potential profits. The monthly continuous flow of funds is expected to be $1200 in profits. In 4 years you would like to have total profits of $100,000. What monthly and effective annual interest rate do you need to make your goal if the interest is compounded continuously?

Answer 1

Monthly profit = $1200

Time = 48 months (4 years)

Future value after 4 years = $100000

Let, monthly interest rate = R

100000 = 1200*((1+R)^48 -1)/R

At R = 2.5%

Future value of profit = $109031.5

At R = 2%

Future value of profit = $95224.22

Using the method of interpolation,

R = 2.5% - ((109031.5 - 100000)/( 109031.5-95224.22))*(2.5% -2%)

R = 2.18%

So, nominal annual interest rate = 2.18%*12 = 26.16%

Since it is compounding continuously, then

Effective annual interest rate = e^(.2616*1) - 1 = 2.718^.2616 - 1

Effective annual interest rate = 29.9%