采用每月等额还本付息办法,

采用每月等额还本付息办法, 采用每月等额还本付息办法，为: 每月还款额=贷款本金×月利率+贷款本金×月利率?(1+月利率)^还款总期数-1 住房按揭贷款等额本息款和等额本金还款计算公式的推导 2006年09月29日 星期五 上午 10:42 等额本息款和等额本金还款计算公式的推导 发表时间: 2006-03-08 22:04:05 住房贷款两种还款方式的计算方式的推导 众所周知，银行住房贷款的分期付款方式分为等额本息付款和等额本金方式付款两种方式。两种付款方式的月付款额各不相同，计算方式也不一样。网上分别有着两种还款方式的计算公式。然而，对于这两个公式的来源却很少有解释，或者解释是粗略的或错误的。本人经过一段时间的思考，终于整明白了其中的原理，并且运用高中数学理论推导出了这两个计算公式。本文将从原理上解释一下着两种还款方式的原理及计算公式的推导过程。 无论哪种还款方式，都有一个共同点，就是每月的还款额(也称月供)中包含两个部分:本金还款和利息还款: 月还款额=当月本金还款+当月利息 式1 其中本金还款是真正偿还贷款的。每月还款之后，贷款的剩余本金就相应减少: 当月剩余本金=上月剩余本金-当月本金还款 直到最后一个月，全部本金偿还完毕。 利息还款是用来偿还剩余本金在本月所产生的利息的。每月还款中必须将本月本金所产生的利息付清: 当月利息=上月剩余本金×月利率 式2 其中月利率=年利率?12。据传工商银行等某些银行在进行本金等额还款的计算方法中，月利率用了一个挺孙子的算法，这里暂且不提。 由上面利息偿还公式中可见，月利息是与上月剩余本金成正比的，由于在贷款初期，剩余本金较多，所以可见，贷款初期每月的利息较多，月还款额中偿还利息的份额较重。随着还款次数的增多，剩余本金将逐渐减少，月还款的利息也相应减少，直到最后一个月，本金全部还清，利息付最后一次，6.2.6 establishing construction site welding secondary, secondary electrode consisted of Rod piled up, welding rod ovens, incubators, thermometers, hygrometers and backing of electrodes, receiving, payment and recovery system. And person responsible for the secondary database. 6.2.7 construction welding machines, grinding machines, plasma cutting machine tool experience is qualified. 6.2.8 welding electrodes, welding wire selection in line with national and industry standards requirements, welding material welding materials quality manual should be provided, its chemical composition, mechanical properties and other indicators should conform to the requirements of the relevant standards, appearance may not have defects such as corrosion, unqualified products cannot be used. 6.2.9 electrode, flux drying before use according to the regulations, and should be kept dry during use, wires should be removed before using the surface oil, rust, etc. Electrodes must not fall off, no rust spots and obvious cracks. 6.3 6.3.1 electrode electrode selection and management list trumpeter argon arc welding electrode arc welding of steel 10# E4303 J427 H08Mn2SiA 20# E4303 J427 H08Mn2SiA Q235-A E4303 J422, H08Mn2SiA 304 E308 A102 H0Cr21Ni10 316L E00-19 A002 H00Cr21Ni10 321 E347 A137 H0Cr21Ni10Ti 1 5Cr ... (2) the purity of argon carbon steel and alloy steel pipe shall not be less than 99.9%. (3) the welding field wind-proof, rain-proof measures must be taken, when the relative humidity is greater than 90%, when the wind speed is greater than 2m/s, do not allow application of argon arc welding, when the wind speed is greater than 8M/s, do not allow the application of arc welding. Welding shall not be less than 0 ? ambient temperature. (4) prior to welding, you should review the lip size, meet the requirements before they 下个月将既无本金又无利息，至此，全部贷款偿还完毕。 两种贷款的偿还原理就如上所述。上述两个公式是月还款的基本公式，其他公式都可由此导出。下面我们就基于这两个公式推导一下两种还款方式的具体计算公式。 1. 等额本金还款方式 等额本金还款方式比较简单。顾名思义，这种方式下，每次还款的本金还款数是一样的。因此: 当月本金还款=总贷款数?还款次数 当月利息=上月剩余本金×月利率 =总贷款数×(1,(还款月数-1)?还款次数)×月利率当月月还款额=当月本金还款，当月利息 =总贷款数×(1?还款次数，(1,(还款月数-1)?还款次数)×月利率) 总利息,所有利息之和 =总贷款数×月利率×(还款次数,(,，,，,，。。。，还款次数,1)?还款次数) 其中1+2+3+…+还款次数,,是一个等差数列，其和为(1，还款次数,,)×(还款次数,,),2,还款次数×(还款次数,,),, 所以，经整理后可以得出: 总利息=总贷款数×月利率×(还款次数，1)?2 由于等额本金还款每个月的本金还款额是固定的，而每月的利息是递减的，因此，等额本金还款每个月的还款额是不一样的。开始还得多，而后逐月递减。 2. 等额本息还款方式 等额本息还款方式的公式推导比较复杂，不过也不必担心，只要具备高中数列知识就可以推导出来了。 等额本金还款，顾名思义就是每个月的还款额是固定的。由于还款利息是逐月减少的，因此反过来说，每月还款中的本金还款额是逐月增加的。 6.2.6 establishing construction site welding secondary, secondary electrode consisted of Rod piled up, welding rod ovens, incubators, thermometers, hygrometers and backing of electrodes, receiving, payment and recovery system. And person responsible for the secondary database. 6.2.7 construction welding machines, grinding machines, plasma cutting machine tool experience is qualified. 6.2.8 welding electrodes, welding wire selection in line with national and industry standards requirements, welding material welding materials quality manual should be provided, its chemical composition, mechanical properties and other indicators should conform to the requirements of the relevant standards, appearance may not have defects such as corrosion, unqualified products cannot be used. 6.2.9 electrode, flux drying before use according to the regulations, and should be kept dry during use, wires should be removed before using the surface oil, rust, etc. Electrodes must not fall off, no rust spots and obvious cracks. 6.3 6.3.1 electrode electrode selection and management list trumpeter argon arc welding electrode arc welding of steel 10# E4303 J427 H08Mn2SiA 20# E4303 J427 H08Mn2SiA Q235-A E4303 J422, H08Mn2SiA 304 E308 A102 H0Cr21Ni10 316L E00-19 A002 H00Cr21Ni10 321 E347 A137 H0Cr21Ni10Ti 1 5Cr ... (2) the purity of argon carbon steel and alloy steel pipe shall not be less than 99.9%. (3) the welding field wind-proof, rain-proof measures must be taken, when the relative humidity is greater than 90%, when the wind speed is greater than 2m/s, do not allow application of argon arc welding, when the wind speed is greater than 8M/s, do not allow the application of arc welding. Welding shall not be less than 0 ? ambient temperature. (4) prior to welding, you should review the lip size, meet the requirements before they 首先，我们先进行一番设定: 设:总贷款额,, 还款次数,, 还款月利率,, 月还款额,, 当月本金还款,,,(,,还款月数) 先说第一个月，当月本金为全部贷款额,,，因此: 第一个月的利息,,×, 第一个月的本金还款额 ,,,,,第一个月的利息 ,,,,×, 第一个月剩余本金,总贷款额,第一个月本金还款额 ,,,(,,,×,) ,,×(,，,),, 再说第二个月，当月利息还款额,上月剩余本金×月利率 第二个月的利息,(,×(,，,),,)×, 第二个月的本金还款额 ,,,,,第二个月的利息 ,,,(,×(,，,),,)×, 第二个月剩余本金,第一个月剩余本金,第二个月本金还款额 ,,×(,，,),,,(,,(,×(,，,),,)×,) ,,×(,，,),,,,，(,×(,，,),,)×, ,,×(,，,)×(,，,),,,，(,，,)×,, 6.2.6 establishing construction site welding secondary, secondary electrode consisted of Rod piled up, welding rod ovens, incubators, thermometers, hygrometers and backing of electrodes, receiving, payment and recovery system. And person responsible for the secondary database. 6.2.7 construction welding machines, grinding machines, plasma cutting machine tool experience is qualified. 6.2.8 welding electrodes, welding wire selection in line with national and industry standards requirements, welding material welding materials quality manual should be provided, its chemical composition, mechanical properties and other indicators should conform to the requirements of the relevant standards, appearance may not have defects such as corrosion, unqualified products cannot be used. 6.2.9 electrode, flux drying before use according to the regulations, and should be kept dry during use, wires should be removed before using the surface oil, rust, etc. Electrodes must not fall off, no rust spots and obvious cracks. 6.3 6.3.1 electrode electrode selection and management list trumpeter argon arc welding electrode arc welding of steel 10# E4303 J427 H08Mn2SiA 20# E4303 J427 H08Mn2SiA Q235-A E4303 J422, H08Mn2SiA 304 E308 A102 H0Cr21Ni10 316L E00-19 A002 H00Cr21Ni10 321 E347 A137 H0Cr21Ni10Ti 1 5Cr ... (2) the purity of argon carbon steel and alloy steel pipe shall not be less than 99.9%. (3) the welding field wind-proof, rain-proof measures must be taken, when the relative humidity is greater than 90%, when the wind speed is greater than 2m/s, do not allow application of argon arc welding, when the wind speed is greater than 8M/s, do not allow the application of arc welding. Welding shall not be less than 0 ? ambient temperature. (4) prior to welding, you should review the lip size, meet the requirements before they ,,×(,，,)^,,,,，(,，,)×,, (1+C)^2表示(1+C)的2次方 第三个月， 第三个月的利息,第二个月剩余本金×月利率 第三个月的利息,(,×(,，,)^,,,,，(,，,)×,,)× , 第三个月的本金还款额 ,,,,,第三个月的利息 ,,,(,×(,，,)^,,,,，(,，,)×,,)×, 第三个月剩余本金,第二个月剩余本金,第三个月的本金还款额 ,,×(,，,)^,,,,，(,，,)×,, ,(,,(,×(,，,)^,,,,，(,，,)×,,)×,) ,,×(,，,)^,,,,，(,，,)×,, ,(,,(,×(,，,)^,×,，,,，(,，,)×,,)×,) ,,×(,，,)^,×(,，,) ,(,，,,，(,，,)×,,×(,，,)) ,,×(,，,)^, ,,,，(,，,)×,，(,，,)^,×,, 上式可以分成两个部分 第一部分:,×(,，,)^,。 第二部分:,,，(,，,)×,，(,，,)^,×,, ,,×,,，(,，,)，(,，,)^,, 通过对前三个月的剩余本金公式进行，我们可以看到其中的规律: 剩余本金中的第一部分,总贷款额×(,，月利率)的,次方，(其中, ,还款月数) 6.2.6 establishing construction site welding secondary, secondary electrode consisted of Rod piled up, welding rod ovens, incubators, thermometers, hygrometers and backing of electrodes, receiving, payment and recovery system. And person responsible for the secondary database. 6.2.7 construction welding machines, grinding machines, plasma cutting machine tool experience is qualified. 6.2.8 welding electrodes, welding wire selection in line with national and industry standards requirements, welding material welding materials quality manual should be provided, its chemical composition, mechanical properties and other indicators should conform to the requirements of the relevant standards, appearance may not have defects such as corrosion, unqualified products cannot be used. 6.2.9 electrode, flux drying before use according to the regulations, and should be kept dry during use, wires should be removed before using the surface oil, rust, etc. Electrodes must not fall off, no rust spots and obvious cracks. 6.3 6.3.1 electrode electrode selection and management list trumpeter argon arc welding electrode arc welding of steel 10# E4303 J427 H08Mn2SiA 20# E4303 J427 H08Mn2SiA Q235-A E4303 J422, H08Mn2SiA 304 E308 A102 H0Cr21Ni10 316L E00-19 A002 H00Cr21Ni10 321 E347 A137 H0Cr21Ni10Ti 1 5Cr ... (2) the purity of argon carbon steel and alloy steel pipe shall not be less than 99.9%. (3) the welding field wind-proof, rain-proof measures must be taken, when the relative humidity is greater than 90%, when the wind speed is greater than 2m/s, do not allow application of argon arc welding, when the wind speed is greater than 8M/s, do not allow the application of arc welding. Welding shall not be less than 0 ? ambient temperature. (4) prior to welding, you should review the lip size, meet the requirements before they 剩余本金中的第二部分是一个等比数列，以(,，月利率)为比例系数，月还款额为常数系数，项数为还款月数,。 推广到任意月份: 第,月的剩余本金,,×(,，,)^, ,,×,,(,,为(,，,)的等比数列的前,项和) 根据等比数列的前,项和公式: ,，,，,,，,,，(((，,,,,,(,,,^,),(,,,) 可以得出 ,×,,,,×(,,(,，,)^,),(,,(,，,)) ,,×((,，,)^,,,),, 所以，第,月的剩余本金,,×(,，,)^,,,×((,，,)^,,,),, 由于最后一个月本金将全部还完，所以当,等于还款次数时，剩余本金为零。 设,,,(还款次数) 剩余本金,,×(,，,)^,,,×((,，,)^,,,),,,, 从而得出 月还款额 ,,,×,×(,，,)^,?((,，,)^,,,) , 总贷款额×月利率×(,，月利率)^还款次数?[(?000保 吕 剩 还款次数,,] 将,值带回到第,月的剩余本金公式中 第,月的剩余本金,,×(,，,)^,,,,×,×(,，,)^,,((,，,)^,,,),×((,，,)^,,,),, ,,×,(,，,)^,,(,，,)^,×((,，,)^,,,),((,，,)^,,,), 6.2.6 establishing construction site welding secondary, secondary electrode consisted of Rod piled up, welding rod ovens, incubators, thermometers, hygrometers and backing of electrodes, receiving, payment and recovery system. And person responsible for the secondary database. 6.2.7 construction welding machines, grinding machines, plasma cutting machine tool experience is qualified. 6.2.8 welding electrodes, welding wire selection in line with national and industry standards requirements, welding material welding materials quality manual should be provided, its chemical composition, mechanical properties and other indicators should conform to the requirements of the relevant standards, appearance may not have defects such as corrosion, unqualified products cannot be used. 6.2.9 electrode, flux drying before use according to the regulations, and should be kept dry during use, wires should be removed before using the surface oil, rust, etc. Electrodes must not fall off, no rust spots and obvious cracks. 6.3 6.3.1 electrode electrode selection and management list trumpeter argon arc welding electrode arc welding of steel 10# E4303 J427 H08Mn2SiA 20# E4303 J427 H08Mn2SiA Q235-A E4303 J422, H08Mn2SiA 304 E308 A102 H0Cr21Ni10 316L E00-19 A002 H00Cr21Ni10 321 E347 A137 H0Cr21Ni10Ti 1 5Cr ... (2) the purity of argon carbon steel and alloy steel pipe shall not be less than 99.9%. (3) the welding field wind-proof, rain-proof measures must be taken, when the relative humidity is greater than 90%, when the wind speed is greater than 2m/s, do not allow application of argon arc welding, when the wind speed is greater than 8M/s, do not allow the application of arc welding. Welding shall not be less than 0 ? ambient temperature. (4) prior to welding, you should review the lip size, meet the requirements before they ,,×,(,，,)^,,(,，,)^,,,((,，,)^,,,) 第,月的利息,第,,,月的剩余本金×月利率 ,,×,×,(,，,)^,,(,，,)^(,,,),,((,，,)^,,,) 第,月的本金还款额,,,第,月的利息 ,,×,×(,，,)^,,((,，,)^,,,),,×,×,(,，,)^,,(,，,)^(,,,),,((,，,)^,,,) ,,×,×(,，,)^(,,,),((,，,)^,,,) 总还款额,,×, ,,×,×,×(,，,)^,?((,，,)^,,,) 总利息,总还款额,总贷款额,,×,,, ,,×,(,×,,,)×(,，,)^,，,,,((,，,)^,,,) 等额本息还款，每个月的还款额是固定的。由于还款初期利息较大，因此初期的本金还款额很小。相对于等额本金方式，还款的总利息要多。 6.2.6 establishing construction site welding secondary, secondary electrode consisted of Rod piled up, welding rod ovens, incubators, thermometers, hygrometers and backing of electrodes, receiving, payment and recovery system. And person responsible for the secondary database. 6.2.7 construction welding machines, grinding machines, plasma cutting machine tool experience is qualified. 6.2.8 welding electrodes, welding wire selection in line with national and industry standards requirements, welding material welding materials quality manual should be provided, its chemical composition, mechanical properties and other indicators should conform to the requirements of the relevant standards, appearance may not have defects such as corrosion, unqualified products cannot be used. 6.2.9 electrode, flux drying before use according to the regulations, and should be kept dry during use, wires should be removed before using the surface oil, rust, etc. Electrodes must not fall off, no rust spots and obvious cracks. 6.3 6.3.1 electrode electrode selection and management list trumpeter argon arc welding electrode arc welding of steel 10# E4303 J427 H08Mn2SiA 20# E4303 J427 H08Mn2SiA Q235-A E4303 J422, H08Mn2SiA 304 E308 A102 H0Cr21Ni10 316L E00-19 A002 H00Cr21Ni10 321 E347 A137 H0Cr21Ni10Ti 1 5Cr ... (2) the purity of argon carbon steel and alloy steel pipe shall not be less than 99.9%. (3) the welding field wind-proof, rain-proof measures must be taken, when the relative humidity is greater than 90%, when the wind speed is greater than 2m/s, do not allow application of argon arc welding, when the wind speed is greater than 8M/s, do not allow the application of arc welding. Welding shall not be less than 0 ? ambient temperature. (4) prior to welding, you should review the lip size, meet the requirements before they