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Math Help - continous income flow, am i right?

  1. #1
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    continous income flow, am i right?

    Question was determine the present value P of a continous income flow of c(t) dollars per year, if c(t)=30000+500t , r=7% , t=5

    note that


    can somone tell me if i did this right? this is a take home question for extra credit and i wanna make sure im right. Im a little confused because i dont know what to put as an answer. do i plug in r and t and get a numer or do i leave the equation for the answer. if i plug in r and t i get -5.451778105X10^10 which looks really wrong lol.



    .
    For the first integral, let so that . Then

    The second integral is integrated by parts: Let and . Then , and using the above work, . So
    . Again using the above work, this becomes
    .
    Putting the above results together
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  2. #2
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    Quote Originally Posted by zerocool18 View Post
    Question was determine the present value P of a continous income flow of c(t) dollars per year, if c(t)=30000+500t , r=7% , t=5

    note that

    can somone tell me if i did this right? this is a take home question for extra credit and i wanna make sure im right. Im a little confused because i dont know what to put as an answer. do i plug in r and t and get a numer or do i leave the equation for the answer. if i plug in r and t i get -5.451778105X10^10 which looks really wrong lol.



    .
    For the first integral, let so that . Then

    The second integral is integrated by parts: Let and . Then , and using the above work, . So
    . Again using the above work, this becomes
    .
    Putting the above results together
    When I substitute t = 5 and r = 7 and do the integration I get 4295.92.
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  3. #3
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    alright , i found an error in my work.
    I see that I messed up the last step. When you put the preceding results together, you should get . Now, when i set r = 0.07 and t = 5, you get which i think is the right answer lol . i wish there was a way i could check this. ive been at this problem for almost 4 hours now =( and i want to atleast see if all my work was worth it.
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