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课 题 基于数学建模的房贷还款方式选择
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院 部 中秋客户祝福短信 数学与计算机科学学院
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二O一四年六月
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基于数学建模的房贷还款方式选择
摘 要
随着我国社会经济不断发展和进步，综合国力不断提升，人民生活水平也在不断改善。但物价，特别是房地产价格，不断攀升也是不争的事实。绝大部分工薪阶层很难一次性现金
购房，于是“住房贷款”、“提前消费”等观念应运而生，融入了人们的生活，按揭贷款方式是人们日常生活中面临的现实问题。
目前，住房贷款还款方式主要有等额本息还款法和等额本金还款法两种。不同的还款方式会产生不同的还款结果。那么，我们该如何根据自己的实际情况，选择出一个合理的、适合自己的还款方式呢？
本文将以现行银行贷款政策和生活金融常识为基础，详细介绍房贷的两种主要还款方式，全面分析还贷计算的相关条件与逻辑关系，将还贷问题转化为数学问题，推导出两种还款法的月供额度、月供本金、月供利息和应偿本金余额等关键数据的计算公式，建立数学模型；根据给定的银行利率和已求出的公式，利用matlab数学软件/Excel;应用软件，计算出20年内平均每个月所需的还款额和所需的本金与利息的总额；根据表格数据分析还款期数与月供额度之间的关系，探讨两种还款方式在利息总额、可贷款总量、利率调整以及提前还款等方面对按揭贷款人的影响，以期贷款人能提高对两种还款法的理性认识，并能结合自身实际选择适当的贷款还款方式，对我们的现实生活具有一定的指导意义和参考价值。
关键词：贷款；利率；等额本息还款；等额本金还款
On mathematical modeling of the mortgage repayment way choice
Abstract
Along with consistent development and constant progress in the social economy, our comprehensive national power is much more strengthened, and our living standard is also much improved. But it is an indisputable fact that prices, especially the real estate prices, have kept rising. And it is difficult for most of the working class to buy a set of apartment by cash. Such terms come into our lives as "housing loans", and “consum非主流文字e in advance”. And mortgage loan becomes a problem in our daily life.
At present, there are two methods for the housing loan repayment, the average capital and interest repayment method and the average capital repayment method. Different repayment methods result in different influences. So, how could we select a reasonable and suitable way for our repayment according to our own actual situations?
On the basis of the current polic上班路上工伤ies for bank loans and记暑假里的一件事 the common sense of daily finance, this paper introduces two main mortgage repayment methods, makes a comprehensive analysis of the loan related conditions and logical relationship to change the loan problem into a math problem, deduces formula of such key data as monthly repayment quota, monthly capital payment, monthly interest payment, and capital balance of the two methods, and sets up the principal balance mathematical model by means of matlab/excel with bank interest rates given and the formula to calculate the average monthly payments and the total amount of the capital and interest required in the loan period of 20 years; and discusses influences of the two repayment methods on the total amount of interest, loan amount, interest rate adjustment with model data, so as to make 6月14日是什么情人节mortgagers aware of rational knowledge of two kinds of payment method, and be able to select an appropriate loan repayment method for their own housing loans.
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