1. Home
  2. >Business Calculus
  3. >Business Integral Application
Help

Continuous money flow

All in One Place

Everything you need for better marks in university, secondary, and primary classes.

Learn with Ease

We’ve mastered courses for WA, NSW, QLD, SA, and VIC, so you can study with confidence.

Instant and Unlimited Help

Get the best tips, walkthroughs, and practice questions.

0/2
?
Intros
Lessons
  1. Continuous Money Flow Overview:
  2. Present and Future Value
  3. Clarifying Revenue Stream
0/3
?
Examples
Lessons
  1. Present and Future value

    Patsy deposits $10000 into a savings account each year for a total of 10 years. If the account earns an interest rate of 10% compounded continuously:

    i) Find the present value

    ii) Find the future value

    1. Suppose the revenue stream is the function f(t)=100e.02tf(t) = 100e^{.02t}, where tt is in years, for a total of 6 years. If the money can earn 3% annual interest compounded continuously:

      i) Find the present value

      ii) Find the future value

      1. Suppose the revenue stream is the function R(t)=1+tR(t) = 1 + t, where tt is in years, for a total of 5 years. If the money can earn 4% annual interest compounded continuously, find the present value.
        Topic Notes
        ?

        In most companies, we want to look at the revenue they invest over time. They will mostly look at the present value, and future value of their investments. To calculate the present value and future value, we use the following formulas:

        PV=∫0TR(t)e−rtdtPV = \int_{0}^{T}R(t)e^{-rt}dt

        FV=erT∫0TR(t)e−rtdtFV = e^{r^{T}}\int_{0}^{T}R(t)e^{-rt}dt

        Where:

        R(t)R(t) = revenue stream

        TT = the total amount of time invested

        rr = interest rate compounded continuously

        Basic Concepts
        ?