房贷月供是采取复利计息还是单利计息?
是这样,今天我计算了一下房贷月供,我本金是65万,年利率是5.5675%,分25年还清,采取等额本息还款方式。银行给的月供是月还4011.66,而我自己用月复利模式(即年金模式)算出来是月供3964.55,而银行给的月供是按月单利模式。想请教各位,我算对了吗?如果是对的,为何银行月供要采取单利模式?我的计算步骤为:1、先根据... 展开
是这样,今天我计算了一下房贷月供,我本金是65万,年利率是5.5675%,分25年还清,采取等额本息还款方式。银行给的月供是月还4011.66,而我自己用月复利模式(即年金模式)算出来是月供3964.55,而银行给的月供是按月单利模式。想请教各位,我算对了吗?如果是对的,为何银行月供要采取单利模式?我的计算步骤为:1、先根据名义年利率计算有效月利率:EAR=(1+5.5675%)^1/12-1;2、用年金现值公式:PV=C/EAR*[1-1/(1+EAR)^(25*12)],得出C=3964.55元;。是不是可以这样认为,如果我计算得是对的,那么银行采取月单利模式比采取月复利模式每月多收约47元,即使按最低利率,0.35%的活期利率,25年下来,相当于多收现值11773元,可以这样理解吗? 收起
其他答案
首先,在公式上,是按照单利计算利息的。但!房贷绝对是复利,因为年利率在折算成月利率时,是没有考虑折现率问题的!其实经济学意义上的单利,是非常少见的!房贷的计息周期是1个月,需要你将当期的本利两清。让我们算一下每个月的房贷构成吧:根据贷款计算器,月供为4017.81中,其中利息为3015.73元(650000*5.5675%/12),本金1002.09,剩余贷款本金648997.92,第二个月就是按 展开
首先,在公式上,是按照单利计算利息的。但!房贷绝对是复利,因为年利率在折算成月利率时,是没有考虑折现率问题的!其实经济学意义上的单利,是非常少见的!房贷的计息周期是1个月,需要你将当期的本利两清。让我们算一下每个月的房贷构成吧:根据贷款计算器,月供为4017.81中,其中利息为3015.73元(650000*5.5675%/12),本金1002.09,剩余贷款本金648997.92,第二个月就是按照剩余的648997.92来计算利息。这样看来,利息是按照本金*利率的方式收取的,符合数学上的单利。为什么说它是复利呢?因为它每期都重新计算一次本金和利息,但其实,每期还的利息也存在折现的问题!这样说明可能好理解些:因为你每个月还的利息,并未让剩余本金减少,仍然算入了下一期应还本金,也就是说你每个月还的利息依然还在计算利息!(虽然你第一个月还了4017.81元,但在次月,只有1002.09元不再计收利息,你还款中的3015.73元,依然在按照月利率收取利息~) 举个例子吧:比方说你借给我2块钱,约定年利率50%,这钱我一直放在手里没花,所以我手上有2块钱。 按道理我一年后给你1块钱的利息,但是你现在要求我半年的时候清一次利息,半年利率25%。于是我在半年的时候给了你5毛钱。 这时候,我手上实际只有1块5了,但年末我还是要再给你5毛钱,虽然利息总额还是1块钱,但后半年的半年利率其实已经是33.33%了!原因为:单利的月利率≠年利率/12!这句话需要一定的理解能力!但还请认真思考:)所以,“单利”其实是极特殊的情况,在实际应用中,是不常见的~关于房贷是复利计算证明如下:根据复利年金系数的公式,算出的复利现值系数是161.779557(((1+5.5675%/12)^300-1)/(5.5675%/12*(1+5.5675%/12)^300)),乘以月供4017.81后,现值为649999.5217元,与贷款额65万一致!所以说,月供还款一定是复利!根据其他回答者的回复,我又计算了该笔贷款月供的复利年金终值系数,((1+5.5675%/12)^300-1)/(5.5675%/12)=648.6483534,乘以月供4017.81后,等于2606145.841元,而根据复利终值系数,65万元,按照5.5675%/12的月利率计算复利,300期后的终值为:650000*(1+5.5675%/12)^300=2606147.758,两者相符。而且65万元,按照5.5675%的年利率计算25年后的复利终值,是2518658.461,小于按月利率计算复利的终值,证明了,年利率/12算月利率本身就是复利~上面的公式说明:假如,每个月都往银行存4017.81,在25年后统一到期,每个月收取利息并将利息再次存入,假如月利率为5.5675%/12,25年后,这笔钱会变成260多万。(这个利率很多短期理财产品都能达到)年金终值等于本金按月计息的复利终值,并大于按年计算的复利终值,佐证了月供这种方式其实是复利,也说明了积少成多的理财理念~题外话:作为房贷专员~对常见的还贷误区,简单答一下!第一:不管是等本还是等额,利息计算的方式都是剩余本金*当期利率,如果逾期未还,是按逾期金额(不是剩余本金)*罚息利率*罚息时间计收罚息。所以,想少还利息,就得多还款!早还款!但是贷款就是因为手上钱不够……能多还还不如少贷了……所以,要做好财务规划!第二:银行一开始利息“收得多”是因为贷款本金高!按照本金余额计息,一开始利息肯定很高!同样期限的贷款,等本方式经常会压得人喘不过气!等本方式在在银行业务规范里的描述是:对还款可能有风险的客户,建议选择等本、降低还款周期,加快还款!但是在实际操作中,为了符合收入还贷比(也即是收入超过月供的2倍),一般会推荐等额还款!这绝对是利人利己的!显示全部 收起
2015-02-12 15:47
来自北京市
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作为一个曾经的房产销售,我负责任地告诉你,是复利,也就是利滚利!而且你最开始前半段每月还款金额绝大多数还的都是利息,只还很少一部分本金,所以复利效果就更明显。以下是根据你所给的数据计算的还款情况。数据数据依次是:期次、偿还本息(元)、偿还利息(元)、偿还本金(元)、剩余本金(元)期次:1还款本息:4017.81还款利息:3015.73还款本金:1002.08剩余本金:648997.9224017. 展开
作为一个曾经的房产销售,我负责任地告诉你,是复利,也就是利滚利!而且你最开始前半段每月还款金额绝大多数还的都是利息,只还很少一部分本金,所以复利效果就更明显。以下是根据你所给的数据计算的还款情况。数据数据依次是:期次、偿还本息(元)、偿还利息(元)、偿还本金(元)、剩余本金(元)期次:1还款本息:4017.81还款利息:3015.73还款本金:1002.08剩余本金:648997.9224017.813011.081006.73647991.1834017.813006.411011.40646979.7844017.813001.721016.10645963.6854017.812997.001020.81644942.8764017.812992.271025.55643917.3374017.812987.511030.30642887.0284017.812982.731035.09641851.9494017.812977.931039.89640812.05104017.812973.101044.71639767.34114017.812968.251049.56638717.78124017.812963.381054.43637663.35134017.812958.491059.32636604.03144017.812953.581064.24635539.79154017.812948.641069.17634470.62164017.812943.681074.13633396.49174017.812938.701079.12632317.37184017.812933.691084.12631233.24194017.812928.661089.15630144.09204017.812923.611094.21629049.88214017.812918.531099.28627950.60224017.812913.431104.38626846.22234017.812908.311109.51625736.71244017.812903.161114.66624622.05254017.812897.991119.83623502.23264017.812892.791125.02622377.20274017.812887.571130.24621246.96284017.812882.331135.49620111.48294017.812877.061140.75618970.72304017.812871.771146.05617824.68314017.812866.451151.36616673.31324017.812861.111156.71615516.61334017.812855.741162.07614354.53344017.812850.351167.46613187.07354017.812844.931172.88612014.19364017.812839.491178.32610835.87374017.812834.021183.79609652.08384017.812828.531189.28608462.80394017.812823.011194.80607268.00404017.812817.471200.34606067.65414017.812811.901205.91604861.74424017.812806.311211.51603650.24434017.812800.691217.13602433.11444017.812795.041222.77601210.34454017.812789.371228.45599981.89464017.812783.671234.15598747.74474017.812777.941239.87597507.87484017.812772.191245.63596262.24494017.812766.411251.40595010.84504017.812760.601257.21593753.63514017.812754.771263.04592490.58524017.812748.911268.90591221.68534017.812743.021274.79589946.89544017.812737.111280.71588666.18554017.812731.171286.65587379.54564017.812725.201292.62586086.92574017.812719.201298.61584788.31584017.812713.171304.64583483.67594017.812707.121310.69582172.98604017.812701.041316.77580856.20614017.812694.931322.88579533.32624017.812688.791329.02578204.30634017.812682.631335.19576869.11644017.812676.431341.38575527.73654017.812670.211347.60574180.13664017.812663.961353.86572826.27674017.812657.681360.14571466.14684017.812651.361366.45570099.69694017.812645.031372.79568726.90704017.812638.661379.16567347.74714017.812632.261385.56565962.19724017.812625.831391.98564570.20734017.812619.371398.44563171.76744017.812612.881404.93561766.83754017.812606.361411.45560355.38764017.812599.821418.00558937.38774017.812593.241424.58557512.81784017.812586.631431.19556081.62794017.812579.991437.83554643.80804017.812573.321444.50553199.30814017.812566.611451.20551748.10824017.812559.881457.93550290.17834017.812553.121464.70548825.47844017.812546.321471.49547353.98854017.812539.491478.32545875.66864017.812532.641485.18544390.48874017.812525.751492.07542898.42884017.812518.821498.99541399.43894017.812511.871505.95539893.48904017.812504.881512.93538380.55914017.812497.861519.95536860.60924017.812490.811527.00535333.59934017.812483.721534.09533799.51944017.812476.611541.21532258.30954017.812469.461548.36530709.94964017.812462.271555.54529154.40974017.812455.061562.76527591.65984017.812447.811570.01526021.64994017.812440.521577.29524444.351004017.812433.201584.61522859.741014017.812425.851591.96521267.781024017.812418.471599.35519668.431034017.812411.041606.77518061.661044017.812403.591614.22516447.441054017.812396.101621.71514825.731064017.812388.581629.24513196.491074017.812381.021636.80511559.691084017.812373.421644.39509915.311094017.812365.791652.02508263.291104017.812358.131659.68506603.601114017.812350.431667.38504936.221124017.812342.691675.12503261.101134017.812334.921682.89501578.211144017.812327.111690.70499887.511154017.812319.271698.54498188.971164017.812311.391706.42496482.541174017.812303.471714.34494768.201184017.812295.521722.29493045.911194017.812287.531730.29491315.621204017.812279.501738.31489577.311214017.812271.431746.38487830.931224017.812263.331754.48486076.451234017.812255.191762.62484313.831244017.812247.011770.80482543.031254017.812238.801779.01480764.021264017.812230.541787.27478976.751274017.812222.251795.56477181.191284017.812213.921803.89475377.301294017.812205.551812.26473565.041304017.812197.141820.67471744.371314017.812188.701829.12469915.251324017.812180.211837.60468077.651334017.812171.691846.13466231.521344017.812163.121854.69464376.831354017.812154.521863.30462513.531364017.812145.871871.94460641.591374017.812137.191880.63458760.961384017.812128.461889.35456871.611394017.812119.691898.12454973.491404017.812110.891906.93453066.561414017.812102.041915.77451150.791424017.812093.151924.66449226.131434017.812084.221933.59447292.541444017.812075.251942.56445349.981454017.812066.241951.57443398.401464017.812057.181960.63441437.771474017.812048.091969.73439468.051484017.812038.951978.86437489.181494017.812029.771988.05435501.141504017.812020.541997.274335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单利。只有超过1个计息周期再付息的才可能采用复利计息。按揭贷款计息周期和还款周期都是1个月,因此是单利。好像很多人没懂,补充一下:什么是复利?利息之上再计息,才是复利。也就是,一个计息周期结束后,尚未付息,便在本金和利息的基础上,计算下一周期的利息。所以超过1个计息周期再付息,才可能采用复利计息(约定按单利计息的情况除外)。按揭贷款计息和还款周期都是1个月。每个月银行计息,你当月还清,因此不存在利 展开
单利。只有超过1个计息周期再付息的才可能采用复利计息。按揭贷款计息周期和还款周期都是1个月,因此是单利。好像很多人没懂,补充一下:什么是复利?利息之上再计息,才是复利。也就是,一个计息周期结束后,尚未付息,便在本金和利息的基础上,计算下一周期的利息。所以超过1个计息周期再付息,才可能采用复利计息(约定按单利计息的情况除外)。按揭贷款计息和还款周期都是1个月。每个月银行计息,你当月还清,因此不存在利息的利息,所以是单利。 收起
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从等额还款计算每期金额的计算公式就可以看出是复利。等额年金的现值等于贷款额。至于每期还款额中分成本金部分和利息部分,只是根据结果倒推而已,不代表每期把利息全部还清了。把不存在利滚利的表象当成是单利没有看清实质。
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