Download the App!
Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.
Question
Answered step-by-step
If income is continuously collected at a rate of $ f(t) $ dollars per year and will be invested at a constant interest rate $ r $ (compounded continuously) for a period of $ T $ years, then the future value of the income is given by $ \int_0^T f(t) e^{r (T - t)}\ dt $. Compute the future value after 6 years for income received at a rate of $ f(t) = 8000 e^{0.04t} $ dollars per year and invested at $ 6.2 \% $ interest.
Video Answer
Solved by verified expert
This problem has been solved!
Try Numerade free for 7 days
Like
Report
Official textbook answer
Video by Brett Boyer
Numerade Educator
This textbook answer is only visible when subscribed! Please subscribe to view the answer
Calculus 2 / BC
Chapter 8
Further Applications of Integration
Section 4
Applications to Economics and Biology
Applications of Integration
Missouri State University
Campbell University
Oregon State University
Lectures
04:26
Future Value of Income If …
04:46
If income is continuously …
04:20
06:19
Find the future value, at …
03:39
Unless stated to the contr…
03:11
Compute the present value …
06:06
Compute the present value…
02:39
A continuous stream of inc…
Okay, so the question gives us the following formula. The integral from zero to capital t of F 50 times e to the R times, the quantity capital, T minus T d t is the future value of income, and then it also gives us half of T R and Capital T and asked us to compete. So, using the formula they gave us, we get integral from 0 to 6 of 1000 e 0.4 t times e to 0.62 times six minus t duty. And this doing one simplification, we're going to get taking out constant terms. And then distributing the exponential is together and combining the light terms, we have this constant factor of e 0.37 to allow. Then everything that's left is a exponential factor left and the integral. And so now we just divide by the coefficient of tea and then keep the exponential term the same and evaluate so writing and out we have 8000 e to 0.372 and you're going to divide at the front was going to be negative. Then we have 0.0 to 2 Times e to minus 0.0 to 2 t taken from 0 to 6. And so when we do that, we have approximately minus 527,000 52.9 times and then plugging in the six and zero get minus 0.124 which finally gives us a future value of approximately 65,000 $230 and 48 cents.
View More Answers From This Book
Find Another Textbook
01:20
Mark takes 2 hours to clean 500 bottles Flor takes 3 hours to clean 450 bott…
02:03
around 420 please join in the volleyball tournament each team shoulder have …
02:13
Maria has seven packages of peanuts. Each pack contains 4/5 cup. She needs 8…
02:11
In a group of students, 30 played chess, 19 played volleyball , 25 played ba…
01:07
suppose that four times the square of a number equals 20 times that number.w…
01:51
3. Mrs. Lao was not able to report in her work due to the Enhanced Community…
23. The width of a rectangle is 6cm shorter than its length. Find the possib…
01:57
Mario will be making a lump sum payment of Php 1.6 million on the condominiu…
01:05
the square of a number decreased by 625 is 0. what is the number?
01:18
Mary is constructing a family tree. She is hoping to trace back through 8 ge…
