Continuous money flow

Continuous money flow

Lessons

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)ertdtPV = \int_{0}^{T}R(t)e^{-rt}dt

FV=erT0TR(t)ertdtFV = 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

  • Introduction
    Continuous Money Flow Overview:
    a)
    Present and Future Value

    b)
    Clarifying Revenue Stream


  • 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


  • 2.

    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


  • 3.
    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.