# Math Help - continous income flow, am i right?

1. ## 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.

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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

2. Originally Posted by zerocool18
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.

3. 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.