Continuous money flow

Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.

Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.

Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

Get the most by viewing this topic in your current grade. Pick your course now.

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