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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|Measuring Interest

Perhaps the most common financial transaction is the investment of a certain amount of money at a specified rate of interest. A person might deposit money in a savings account with the expectation of earning interest on the amount deposited. Conversely, a bank makes loans with the expectation of being paid interest in addition to repayment of the principal. The term principal refers to the value of the loan/deposit at the time the transaction is made. The term present value is also used in this context.

In each case the interest is paid in compensation for the use of funds during the period of the transaction. The initial deposit or loan is called the principal and the total amount paid back after a period of time is called the accumulated value. The difference between the accumulated value and the initial deposit is the amount of interest.
Example 2.1 A loan of $\$ 1,000$is paid off with ten equal payments of$\$120$ each. What is the principal for this transaction? What is the amount of interest paid? Can we compute the interest rate for this transaction?
Solution: The principal is the amount of the loan: $\$ 1,000$. The payments total$\$1,200$ on a principal of $\$ 1,000$so the interest paid is$\$200$. Although $\$ 200$is$20 \%$of$\$1,000$, the interest rate on this loan is almost certainly not $20 \%$. To compute the interest rate we need to know when the payments took place. We will discuss the computation of interest rates for loans in Chapter 5. We begin this chapter by discussing the various ways interest is computed when a single deposit is made and later withdrawn. Later, we will discuss those (much more common) cases where deposits and withdrawals occur throughout the period of an investment.

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|The Accumulation and Amount Functions

We assume an amount $P_o$ is deposited and wish to compute the value of this deposit at any time in the future. The initial amount is also known as the principal or present value $(P V)$ while the value at a later date is known as the accumulated amount or future value $(F V)$. The difference between the accumulated amount and the principal is the interest earned (or paid – it all depends on whose point of view you take!) on the transaction.
$$\text { Interest Paid(earned })=I=F V-P V$$
Example 2.2: $\$ 500$is deposited in a savings account at Big Olde Bank. Three years later, the account has an accumulated value of \$546.36. Discuss the situation from the point of view of
a) the customer
b) the bank.
Solution:
a) From the point of view of the customer, the interest earned is $\$ 46.36$. b) From Big Olde Bank’s point of view, the interest paid is$\$46.36$. Big Olde Bank will need to find a way to put the $\$ 500$to work so as to earn at least$\$46.36$ in order to turn a profit on this transaction.

In almost all cases, the accumulated amount will depend on the length of time between deposit and withdrawal. We will use the letters $t$ and $n$ for the length of time of a given transaction. In general, $n$ will indicate an integral number of some time measurement, e.g., 3 years or 7 months. By contrast, $t$ will be used in cases where the time period is not assumed to be an integer, e.g., $3.7$ years or $14.56$ days.

The unit in which time is measured is known as the period or the interest conversion period. We can measure time using any time period provided we make it clear what that period is. Time is measured in years unless stated otherwise. When working problems it is important to determine the interest conversion period first. Finally, while we will often consider the case when $t$ is an integer $(0,1,2,3 .$.$) , all of the analysis applies if t$ is any real number.
NOTE: In some cases interest can only be withdrawn at integer time periods. You will encounter this on some FM problems. In some cases a different formula is used to calculate the interest earned during a fractional period.

# 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 and Amount Functions

已付利息（赚取 )=我=F在−磷在

b) 从 Big Olde Bank 的角度来看，支付的利息是$46.36. 大奥尔德银行将需要找到一种方法将$500工作以赚取至少\$46.36为了在这笔交易中获利。

## 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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