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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

## 经济代写|精算科学代写Actuarial Science代考|Discount Rates

In some cases, interest is paid at the inception of the loan, rather than at the end. PayDay loan establishments often operate in this fashion. This decreases the default risk (sometimes called the exposure) of the loan. Here are two scenarios:

Loan 1: $\$ 500$is borrowed for a year at an effective rate of interest of$6 \%$. At the end of the year, the borrower pays the lender$\$530$.

Loan 2: $\$ 500$is borrowed for a year, but the borrower pays the interest at the loan’s inception. The borrower receives$\$470$ and must repay $\$ 500$at the end of one year. In both cases the interest paid is$\$30$. However in the second case the interest is paid on a loan of only $\$ 470$. Loan 2 is an example of computing interest as a discount and is said to have an effective rate of discount of$6 \%$. The effective rate of discount is a measure of interest which is paid at the beginning of the period. The symbol for the rate of discount is$d$. Note that$d$computes an amount which is paid at the beginning but is based on the amount at the end of the period. In our example Loan 2 required a payment of$\$30$ which is $6 \%$ of the $\$ 500$loan but$6.3829 \%$of the$\$470$ which the borrower receives.

## 经济代写|精算科学代写Actuarial Science代考|Nominal Rate of Discount

If interest is computed at discount and is compounded $p$ times per interest period we denote the nominal rate of discount per period as $d^{(p)}$ and have the relation
$$\left(1-\frac{d^{(p)}}{p}\right)^{p}=1-d$$
We can combine the information so far into a single equation which enables one to convert to and from nominal rates of discount to nominal rates of interest
$$\left(1+\frac{i^{(m)}}{m}\right)^{m}=1+i=\frac{1}{v}=\frac{1}{1-d}=\left(1-\frac{d^{(p)}}{p}\right)^{-p}$$
Finally, we have the following relationships among discounts and interest rates compounded at any rate.

# 精算科学代考

## 经济代写|精算科学代写Actuarial Science代考|Nominal Rate of Discount

(1−d(p)p)p=1−d

(1+一世(米)米)米=1+一世=1在=11−d=(1−d(p)p)−p

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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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