Project

Continuos Money Flow

(Amount and Accumulated Present Value)

1. Accumulated Amount of a continuous money flow:

Money is flowing continuously into a savings account at an annual rate of $1000 at interest rate 7.5%, compounded continuously.

(a) Determine the 'Continuous-Money-Flow function' f(x), of the continuous money flow described above, where x represents time.

(b) Graph the ''Continuous-Money-Flow function' f(x), the line y = 1000, and the line

x =15.

(c) What does the area of the rectangle formed by the lines y = 1000, x =15 , the y-axis,

and the x-axis represent?

(d) What does the area above the rectangle and below the curve represent?

(e) What does the entire area under the curve represent?

(f) Evaluate the integral of the Amount-function from x = 0, to x = 15.

(g) What does the value of the integral represent?

2. Accumulated Present Value of a continuous money flow:

A man takes a job as a truck driver at the age of 25. He has an annual salary of $34,000 that is paid in a continuous money flow. The current interest rate is 7%, compounded continuously. The man plans to retire at the age of 65.

(a) Determine the 'Present-Value-function' g(x), of the continuous money flow, where x represents time.

(b) Graph the 'Present-Value-function' g(x), and the line x = 40.

(c) What does the area of the region formed by the 'Present-Value-function' g(x), the line x = 40 , the y-axis, and the x-axis represent?

(d) Evaluate the integral of the Present-Value-function from x = 0, to x = 40.

(e) What does the value of the integral represent?