Actuarial Study on Equal Progressive and Equal Ratio Progressive Repayment Model
Authors: Liu Yongkuo 
Published: April 2021

Abstract
Equal progressive repayment method and equal ratio progressive repayment method are two kinds of repayment modes which are widely used in countries and regions where individual housing loan businesses flourish internationally. Firstly, starting from cash flow generated during repayment process, modeling loan repayment process, obtains relations between payment, principal and interest in general repayment mode; secondly, uses relational formula to generate equal progressive (withdrawal) repayment method and equal ratio progressive (withdrawal) repayment method next payment, principal and interest mathematical expression; Finally through case analysis give two kinds of repayment methods applicable to housing groups provide reference for financial institutions to introduce diversified repayment methods.When buyers handle mortgage loans, financial institutions generally offer two kinds of repayment methods: equal principal repayment method and equal principal repayment method. Equal principal repayment means equal amounts of loans within repayment periods, repayment of principal amount per month (month) and interest generated during that period, i.e. fixed assets per month (month). Equal interest payment method is to add principal sum of mortgage loan sum interest sum then share each repayment period (month) namely each period of period for fixed. With rapid economic development of our country, residents’ consumption demand has changed greatly, and the concept of advanced consumption gradually accepted by people. Financial institutions have created many new types of loan repayment methods to satisfy people’s consumption demand such as single debt service payment maturity repayment method equal progressive repayment method mobile combination repayment method check-in payment method double week supply relay loan circulation loan balloon loan hole loan etc. Most of these innovative repayment methods are used in short-term consumer loans while residents mortgage loans are long term loans and belong to banks’ high quality assets. Shao Lei and Mr Chen Yonghong pointed out that from America Japan and Hong Kong China such as private housing mortgage lending business booming countries and regions actual situation such as progressive repayment method and equal progressive repayment method is one of two most popular repayment modes internationally especially welcomed by newly married couples and young entrepreneurs. However, these two kinds of repayment methods are complicated, coupled with computer settings and other reasons, currently in China temporarily less used by banks.In our country loan consumption mode gradually accepted by ordinary people. In our country common loan repayment mode includes one-time repayment method equal principal interest repayment method equal principal repayment method. Besides three common repayment modes mentioned above, there are other kinds of progressive repayment methods and equal progressive repayment methods which are commonly used internationally, although these two kinds of repayment methods are less used by banks in China than in China. However, in countries where individual loan business flourish, two kinds of consumer credit repayment modes are very popular. This paper establishes mathematical models of equal ratio progressive repayment method and equal progressive repayment method by using annuity theory in financial mathematics, and analyzes the suitable crowd of these two kinds of repayment methods.