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 7 years, then the future value of the income is given by x [ f(t) =² f(t) er(T-t)dt. Compute the future value (in dollars) after 8 years for income received at a rate of f(t) = 7,000e dollars per year and invested at 6.5% interest. (Round your answer to the nearest cent.) 0.03
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 7 years, then the future value of the income is given by x [ f(t) =² f(t) er(T-t)dt. Compute the future value (in dollars) after 8 years for income received at a rate of f(t) = 7,000e dollars per year and invested at 6.5% interest. (Round your answer to the nearest cent.) 0.03
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Q 8.4 #5
![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 (in dollars) after 8 years for income received at a rate of \( f(t) = 7{,}000e^{0.03t} \) dollars per year and invested at 6.5% interest. (Round your answer to the nearest cent.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9da2e264-a1e6-46b0-be14-3a843a696338%2F09613a63-be24-471e-b835-156e9877ecea%2Fexpbdbc_processed.png&w=3840&q=75)
Transcribed Image Text: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 (in dollars) after 8 years for income received at a rate of \( f(t) = 7{,}000e^{0.03t} \) dollars per year and invested at 6.5% interest. (Round your answer to the nearest cent.)
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