Solve the problem.
-Find the future value at 9% interest compounded continuously for five years for the continuous income stream with rate of flow f(t) = 750. (Round answer to the nearest dollar.)
A) $750
B) $4736
C) $474
D) $47,359

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 $f(t) = 750$, $r = 0.09$, and $T = 5$, the future value is found by integrating $750e^{0.09(5-t)}$ from $0$ to $5$. This results in a future value of approximately $4736 when rounded to the nearest dollar.

Solve the Problem. -Find the Future Value at 9% Interest Compounded Continuously for Compounded