mooc课程mit 6.00.1xproblem set2解决方法

• PAYING THE MINIMUM
  计算每月信用卡最低还款额及剩余应还款额

  balance = 4842 #还款额
  annualInterestRate = 0.2 #年利息比率
  monthlyPaymentRate = 0.04 #每月最低还款比率
  total = 0
  #循环计算1-12月
  for month in range(1, 13):
      payment = monthlyPaymentRate * balance
      total += payment
      balance = (balance - payment) * (1 + annualInterestRate / 12.0)
      print "Month:", month
      #round(x,2)保留x两位小数
      print "Minimum monthly payment:", round(payment, 2)
      print "Remaining balance:", round(balance, 2)
  
  print "Total paid:", round(total, 2)
  print "Remaining balance:", round(balance, 2)

• PAYING DEBT OFF IN A YEAR
  保持最低还款时查找一年最低的利息

  balance = 3926 #还款额
  annualInterestRate = 0.2 #年利息率
  payment = 0
  b = 1
  
  while b > 0:
      payment += 10
      b = balance
  
      for month in range(1, 13):
          b = (b - payment) * (1 + annualInterestRate / 12.0)
  
  print "Lowest Payment:", payment

• USING BISECTION SEARCH TO MAKE THE PROGRAM FASTER
  使用二分法优化上个问题的实现效率

  balance = 999999
  annualInterestRate = 0.18
  
  low = balance / 12.0
  high = (balance * (1 + annualInterestRate / 12.0)**12) / 12.0
  
  payment = (high + low) / 2.0
  b = balance
  for month in range(1, 13):
      b = (b - payment) * (1 + annualInterestRate / 12.0)
  
  while abs(b) > 0.01:
      if b < 0:
          high = payment
      else:
          low = payment
  
      payment = (high + low) / 2.0
      b = balance
      for month in range(1, 13):
          b = (b - payment) * (1 + annualInterestRate / 12.0)
  
  print "Lowest Payment:", round(payment, 2)