Homework:HW 16.32 of 8 ### Understanding Continuous Compounding and Money Flow RateThe function $ f(x) = 1300 $ represents the rate of flow of money in dollars per year. We will work under the assumption of a 10-year period with an interest rate of 8% compounded continuously. Our objectives are to find: (A) The present value.(B) The accumulated amount of money flow at $ t = 10 $.**(A) The present value is $ [input box] **(Do not round until the final answer. Then round to the nearest cent as needed.)### Explanation1. **Compounded Continuously:** Understanding continuous compounding is essential for financial calculations, especially when interest is compounded without interruption over a period.2. **Function Representation:** The given function $ f(x) = 1300 $ is a constant function representing the rate of flow of money. This means that every year, $1300 is the inflow rate.3. **Interest Rate and Period:** - **Interest Rate (continuous):** 8% or 0.08 as a decimal - **Time Period (t):** 10 years ### Formulae to Note\[ PV = \int_0^{10} 1300 \cdot e^{-0.08t} dt \]Where $ PV $ is the present value, and $ e $ denotes the base of the natural logarithm.### Calculation Steps1. Integrate the given flow rate function with the exponential decay factor accounting for continuous compounding.2. Compute the integral using appropriate limits and substitute to find the exact present value.Following these steps accurately will yield the present value which is then to be rounded to the nearest cent as necessary. By placing emphasis on accurate intermediate steps without rounding prematurely, we will ensure precision in the results for educational purposes.

Name: Homework:HW 16.32 of 8 ### Understanding Continuous Compounding and Mo
Uploaded: 2024-03-20T06:38:44.000Z
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Description: Homework:HW 16.32 of 8 ### Understanding Continuous Compounding and Money Flow RateThe function $ f(x) = 1300 $ represents the rate of flow of money in dollars per year. We will work under the assumption of a 10-year period with an interest rate of