最近在看《Python编程导论》（第二版）， 看到类那一章时，后面有个对比几种不同类型贷款的例子，有一天在回看时，突然发现，这不就是一种量化的方式么？之前本来是草草地一带而过，现在又来了兴趣，打算仔细研究研究。

注：本文对书中原有的代码基本不做改动，主要通过注释的方式进行说明，并增加了另一种贷款方式进行比较，旨在帮助大家对代码做进一步分析。

def findPayment(loan, r, m):# 计算在贷款额loan 月利率r和期限m个月下,每月需返还的固定金额return loan * ((r * (1 + r) ** m) / ((1 + r) ** m - 1))

class Mortgage(object):# 构建贷款类, 定义四种贷款都有的属性def __init__(self, loan, annRate, months):self.loan = loan    # 贷款总额self.rate = annRate / 12    # 将年利率转化为月利率self.months = months    # 还款月数self.paid = [0.0]   # 已支付金额self.outstanding = [loan]    # 剩余本金self.payment = findPayment(loan, self.rate, months)    # 每月还款金额， 默认按照等额本息的方式self.legend = None    # 贷款描述def makePayment(self):# 还款函数，调用此函数进行还款self.paid.append(self.payment)reduction = self.payment - self.outstanding[-1] * self.rate    # 还款金额中的本金self.outstanding.append(self.outstanding[-1] - reduction)    # 记录剩余本金def getTotalPaid(self):# 返回已支付贷款总额return sum(self.paid)def __str__(self):# 返回贷款描述return self.legend

class Fixed(Mortgage):
# 等额本息子类
# 只需继承Mortgage()，重写描述属性self.legend即可def __init__(self, loan, r, months):Mortgage.__init__(self, loan, r, months)self.legend = "等额本息, " + str(round(r * 100, 2)) + '%'

def totalCapitalPayment(loan, months, r):
# 等额本金类贷款每个月要还的本金不变，而利息是随着还款月数的增加而减少的，所以定义一个函数，直接返回一个包含每月还款金额的列表即可total = []for m in range(months):total.append(loan / months + (loan - m * (loan / months)) * r)return totalclass FixedCapital(Mortgage):# 等额本金子类def __init__(self, loan, r, months):Mortgage.__init__(self, loan, r, months)# self.payment =capitalPayment(loan, r, months)self.capital = loan / monthsself.total = totalCapitalPayment(loan, months, self.rate)self.legend = "等额本金, " + str(round(r * 100, 2)) + '%'def makePayment(self, m):# 由于等额本金的每月还款额与当前还款月数相关，所以引入还款月数mself.paid.append(self.total[m])# 本期剩余本金 = 上期剩余本金 - 每月固定本金self.outstanding.append(self.outstanding[-1] - self.capital)

class FixedWithPts(Mortgage):# 固定点数子类def __init__(self, loan, r, months, pts):Mortgage.__init__(self, loan, r, months)self.pts = pts    # 固定点数# 计算第一次按照固定点数还款的金额self.paid = [self.loan * (self.pts / 100)]self.legend = "固定点数, " + str(round(r * 100, 2)) + '%, ' + str(pts) + ' points'

class TwoRate(Mortgage):# 双利率子类def __init__(self, loan, r, months, teaserRate, teaserMonths):Mortgage.__init__(self, loan, teaserRate, months)self.teaserMonths = teaserMonths    # 前期低利率月数self.teaserRate = teaserRate    # 前期低利率self.nextRate = r / 12    # 后期高利率self.legend = '双利率, ' + str(teaserRate * 100) + '% for ' + str(self.teaserMonths) + ' months, then ' + \str(round(r * 100, 2)) + '%'def makePayment(self):# 如果到达teaserMonths，则使用self.nextRate高利率，后面每月的付款金额按照剩余本金、利率和月数重新计算if len(self.paid) - 1 == self.teaserMonths:self.rate = self.nextRateself.payment = findPayment(self.outstanding[-1], self.rate, self.months - self.teaserMonths)Mortgage.makePayment(self)    # 未到达teaserMonths时，每月的还款金额

# 比较结果
Fixed, 7.0%
Total payments = $479017
Fixed Capital, 7.0%
Total payments = $410583
Fixed, 5.0%, 3.25 points
Total payments = $393011
4.5% for 48 months, then 9.5%
Total payments = $551444

从比较结果可以看出，还款总额从高到低依次为：

双利率 >  等额本息 > 等额本金 > 固定点数

def plotPayments(self, style):
# 统计每月还款额pylab.plot(self.paid[1:], style, label=self.legend)def plotTotPd(self, style):
# 统计每月还款总额totPd = [self.paid[0]]for i in range(len(self.paid)):totPd.append(totPd[-1] + self.paid[i])pylab.plot(totPd, style, label=self.legend)def plotBalance(self, style):
# 统计每月剩余本金pylab.plot(self.outstanding, style, label=self.legend)def plotNet(self, style):# 统计每月支付总利息totPd = [self.paid[0]]for i in range(1, len(self.paid)):totPd.append(totPd[-1] + self.paid[i])# 先通过数组计算出每月偿还的本金（贷款总额 - 每月剩余本金）equityAcquired = pylab.array([self.loan] * len(self.outstanding)) - pylab.array(self.outstanding)# 再用每月的总还款额 - 每月偿还本金 = 每月偿还利息net = pylab.array(totPd) - equityAcquiredpylab.plot(net, style, label=self.legend)

def plotMortgages(morts, amt):def labelPlot(figure, title, xLabel, yLabel):pylab.figure(figure)        # 指定当前图，即绘制前要先指定图的figure值pylab.title(title)          # 设置标题pylab.xlabel(xLabel)        # 设置x轴标签pylab.ylabel(yLabel)        # 设置y轴标签pylab.legend(loc='best')    # 将描述信息放在不与曲线冲突的最合适区域styles = ['k-', 'k-.', 'k:', 'b-']              # 设置各类贷款对应的曲线样式payments, cost, balance, netCost = 0, 1, 2, 3   # 设置图的figure，对各类曲线按照指标分类for i in range(len(morts)):pylab.figure(payments)              # 根据figure值，将各类曲线绘制到对应的图中morts[i].plotPayments(styles[i])    # 月还款额pylab.figure(cost)morts[i].plotTotPd(styles[i])       # 总还款额pylab.figure(balance)morts[i].plotBalance(styles[i])     # 剩余本金pylab.figure(netCost)morts[i].plotNet(styles[i])         # 月支付利息labelPlot(payments, '贷款' + str(amt) + '元的每月还款情况', '月数', '月还款金额')labelPlot(cost, '贷款' + str(amt) + '元的还款总额', '月数', '已支付金额')labelPlot(balance, '贷款' + str(amt) + '元的每月本金剩余情况', '月数', '剩余未还本金')labelPlot(netCost, '贷款' + str(amt) + '元的累计利息支付情况', '月数', '支付的累计利息')

可以看出，等额本息和固定点数从始至终都维持着恒定的还款金额，但是由于固定点数提前还了一部分的贷款，所以后期支付的金额就会少一些；

该图反映了总还款额随时间变化的情况。如果对比最后贷款结束时的还款金额，很明显，固定点数 < 等额本金 < 等额本息 < 双利率。