Solve the problem.
-Find the future value at 8% interest compounded continuously for five years for the continuous income stream with rate of flow f(t) = 560. (Round answer to the nearest dollar.)
A) $3443
B) $835
C) $2308
D) $2750

Question

Quizplus · Accepted Answer

The future value of a continuous income stream, when interest is compounded continuously, is calculated using the formula $FV = \int_{0}^{T} f(t) e^{r(T-t)} dt$, where $f(t)$ is the rate of flow of the income, $r$ is the annual interest rate, and $T$ is the time in years. For $f(t) = 560$, $r = 0.08$, and $T = 5$, the future value is calculated as $FV = 560 \int_{0}^{5} e^{0.08(5-t)} dt$. Solving this integral gives a future value of approximately $3443 when rounded to the nearest dollar.

Solve the Problem. -Find the Future Value at 8% Interest Compounded Continuously for Compounded