mooc课程mit 6.00.1x--problem 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)