# Continuous stream of income?

• Feb 20th 2010, 09:19 PM
Quixotic
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 $\displaystyle 80e^{-.08t}$ and the interest rate is 10%.

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

but I cannot figure out how integrate this. Am I setting up the problem wrong?
• Feb 21st 2010, 12:05 AM
ione
Quote:

Originally Posted by Quixotic
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 $\displaystyle 80e^{-.08t}$ and the interest rate is 10%.

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

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

$\displaystyle e^a e^b=e^{a+b}$

so $\displaystyle \int\ 80e^{-.08t} e^{-.10t} dt=\int\ 80e^{-.18t} dt$