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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

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|The Accumulation Function

If we deposit $P V=P_0$ units instead of just 1 , the accumulated amount is given by the amount function:
The Amount Function
$$A(t)=P_0 \cdot a(t)$$
If we denote the initial deposit (principal) by $P V$ as is common and the accumulated amount by $F V$, we can write this as
The Amount Function Using FV and PV Notation
$$F V=A(t)=P V \cdot a(t)$$
In general, the dollar amount of interest earned varies from period to period ${ }^1$. We denote the amount of interest earned during the $n^{\text {th }}$ period by $I_n$. Since the first period is from $t=0$ to $t=1$, the $n^{\text {th }}$ period is the time from $t=n-1$ to $t=n$. We can compute $I_n$ using our basic definition of interest as the difference between the initial and final principal amounts. In this case we have
Interest Earned in the $n^{\text {th }}$ Period
$$I_n=A(n)-A(n-1)=P_0 \cdot(a(n)-a(n-1))$$

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|The Effective Rate of Interest

Definition: The effective rate of interest for a given period is the amount of money that one unit of principal invested at the start of a particular period will earn during that one period. It is assumed that interest is paid at the end of the period in question ${ }^2$.

If the period is one year, the effective rate of interest is also referred to as the effective annual rate of interest. This is sometimes called the APR (annual percentage rate) when expressed as a percentage. An annual effective rate of $.05$ would correspond to an APR of $5 \%$. As we shall see, the APR reported by various consumer credit companies is not always the same as the effective annual rate. As a result, we will use the term effective annual interest rate (or effective monthly interest rate or …) except during our discussion of the Truth in Lending Laws at the end of Chapter 6 .

We will use the symbol $i$ for the effective rate of interest. Again, unless stated otherwise, the period is assumed to be one year. In terms of $a(t)$ we have $i=a(1)-a(0)=a(1)-1$ so we have:
Effective Rate of Interest, $i_1$ in period 1
$$i_1=a(1)-1$$
We can express $i$ in terms of $A(t)$ as well. Since $A(t)=P_0 a(t)$ we have:
\begin{aligned} i_1 &=\frac{a(1)-a(0)}{a(0)} \ &=\frac{\frac{A(1)}{P_0}-\frac{A(0)}{P_0}}{\frac{A(0)}{P_0}} \ &=\frac{A(1)-A(0)}{A(0)} \end{aligned}
Example 2.4: A deposit of $\$ 550$earns$\$45$ in interest at the end of one year. What is the effective annual interest rate?
Solution: We use Equation $2.7$
$$i_1=\frac{A(1)-A(0)}{A(0)}=\frac{595-550}{550}=.08182$$
This would typically be expressed as a percentage: $8.182 \%$.

# 金融数学代考

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|The Accumulation Function

$$A(t)=P_0 \cdot a(t)$$

$$F V=A(t)=P V \cdot a(t)$$

$$I_n=A(n)-A(n-1)=P_0 \cdot(a(n)-a(n-1))$$

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|The Effective Rate of Interest

$$i_1=a(1)-1$$

$$i_1=\frac{a(1)-a(0)}{a(0)} \quad=\frac{\frac{A(1)}{P_0}-\frac{A(0)}{P_0}}{\frac{A(0)}{P_0}}=\frac{A(1)-A(0)}{A(0)}$$

$$i_1=\frac{A(1)-A(0)}{A(0)}=\frac{595-550}{550}=.08182$$

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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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