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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 金融代写|金融数学代写Financial Mathematics代考|Interest Rates, Future Values, and Compounding Methods

The previous discussion made interest rates sound easy: the interest rate that equates $\$ 100$today with$\$120$ in one year was reported as being $20 \%$. But interest rate methods are made complex by compounding. Compounding is the practice of interest being assessed on interest. It makes economic sense that the dollar compensation received for lending or paid for borrowing should be adjusted through time as the size of the accrued money grows. Ignoring compounding is known as using simple interest and is sometimes used for low interest rates and short periods of time. Simple interest is illustrated in Equation 2.1, defining $T$ as the number of years between the present and future values:
$$F V_T=P V \times(1+r T)$$
where $F V_T$ is the future value in $T$ years, $P V$ is the present or current value (year 0 ), and $r$ is the annual interest rate. For longer-term time horizons $(T$ ), it makes sense for interest to be compounded periodically such as annual compounding which is depicted in Equation 2.2:
$$F V_T=P V \times(1+r)^T$$
Example 2.1: If $T$ is 2 and $r$ is $8 \%$, find the future value of $\$ 1,000$assuming annual compounding. $$F V_2=P V(1+r)^2=\ 1,000(1.08)^2=\ 1,000(1.1664)=\ 1,166.40$$ Financial calculators and spreadsheets make these computations and the ones that follow very easy. Interest is such an important expression of the value of money through time that in most financial practices compounding is performed more often than annually. Equation$2.3$expresses a general formula for discrete compounding called m periods per year compounding. ## 金融代写|金融数学代写Financial Mathematics代考|Discounting and Present Values Future values were used in the previous section to introduce the time value of money because the idea of an investment value growing through time is intuitively easy. But in finance in general and in this book the more common application is in the computation of present values, called discounting. A present value is the market value today of one or more cash flows to be received on a deferred basis when taking into account market interest rates. A present value can be computed or discounted from a future value by simply reversing the computation of FV from the previous section into the computation of PV (given FV). The present value of a cash flow is equal to the future value multiplied by the time value discount factor. For example, using annual compounding and rearranging Equation 2.2: $$P V=\Gamma V_T(1+r)^{-T}$$$(1+r)^{-T}$is called time value discount factor and is the multiplying factor to bring future cash flows to today. Example 2.5: If$T$is$2, r$is$8 \%$, assuming annual compounding and$F V_T=\$1,000$, then:
$$P V=\ 1,000(1.08)^{-2}=\ 1,000 /(1.1664)=\ 857.34$$
The case of continuous compounding to calculate a present value (i.e., discount a cash flow) is shown in Equation 2.6:
$$P V=F V_T \times e^{-r T}$$
$e^{-r T}$ is a time value discount factor.

# 金融数学代考

## 金融代写|金融数学代写Financial Mathematics代考|利率，未来价值和复利方法

.

$$F V_T=P V \times(1+r T)$$

$$F V_T=P V \times(1+r)^T$$

$$P V=\ 1,000(1.08)^{-2}=\ 1,000 /(1.1664)=\ 857.34$$

$$P V=F V_T \times e^{-r T}$$
$e^{-r T}$是时间价值贴现因子

## 有限元方法代写

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

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