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Math Help - Continuous stream of income?

  1. #1
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    Continuous stream of income?

    I have a practice problem that has me utterly confused.

    I am suppose to find the present value of a continuous stream of income over 5 years if the rate of income is  80e^{-.08t} and the interest rate is 10%.

    I suspect the problem should be set up this way:
     <br />
\int\  80e^{-.08t} e^{-.10t} dt <br />

    but I cannot figure out how integrate this. Am I setting up the problem wrong?
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  2. #2
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    Quote Originally Posted by Quixotic View Post
    I have a practice problem that has me utterly confused.

    I am suppose to find the present value of a continuous stream of income over 5 years if the rate of income is  80e^{-.08t} and the interest rate is 10%.

    I suspect the problem should be set up this way:
     <br />
\int\ 80e^{-.08t} e^{-.10t} dt <br />

    but I cannot figure out how integrate this. Am I setting up the problem wrong?
    I don't know if the problem is set up correctly but

    e^a e^b=e^{a+b}

    so \int\ 80e^{-.08t} e^{-.10t} dt=\int\ 80e^{-.18t} dt
    Last edited by ione; February 21st 2010 at 09:37 AM.
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