Compound Interest

• Interest computed on the principal and any accumulated interest is called compound interest
• A = p(1+r/n)^nt
  • A = amount ( p+i)
  • p = principal
  • r = interest rate
  • n = number of compounding periods per year
  • t = time in years.
• Problems 7 through 14
• Effective Annual yield or annual percentage yield is the simple interest rate that gives the same amount of interest as a compound rate over the same period of time.
• problem 31

          p = $1, t =1, n = 12, r = 3.5%
  
  	A=1(1+3.5/12)^(12*1) =  1.0356
  	i = A-1 = .0355 = 3.56%
  	
   
      

• The present value formula is used to determine how much must be deposited now to achieve a final amount later.
• p = A/(1+r/n)^nt
• Same formula
• See problem 15

Installment Buying

• We will deal with loans for a fixed period of time.
• We need the table on page 680.
• I will provide this table with the test if you need it.
• To use this table, calculate the number of $100 in the loan.
• Look it up in the finance charge per $100.
• Multiply by the number of $100 in the loan.
• This is the finance charge.
• Add this to the amount financed, this is the amount o repay
• Divide this by the payments, this is the monthly payment.
• Problem number 11

         Becky wants 9,900
         She puts 10% down
           9900 x .1 = $990
  	 9,900 - 990 = 8,910
         Find finance charge per $100
            t = 48 months
  	  r = 9.5%
  	  Look this up f= 20.59
        Calculate the $100s in the loan  8910/100 = 89.1
        Calculate the finance charge   89.1 x 20.59 = 1,834.57
        Calculate the total amount    8,910+ 1,834.57 = 10,744.57
        Calculate the monthly payment   10,744.57/12 = 223.85 
      

• Paying off a loan early: The Actuarial Method.
• u = n*P*V/(100+V)
  • u is the unearned interest (interest you don't have to pay)
  • n is the number of payments remaining
  • P is the monthly payment
  • V is the value from the the table corresponding to the payments remaining
• Example: Problem 17

          P = 12,000   (120 $100)
  	Monthly payment = $232
  	Months = 60
  
  	Total of loan is 60*232 = 13,920
  	Finance Charge = 12,000 - 13,920 = 1,920
  	Finance Charge / $100 = 1,920/120 = 16 
  	(Find this in the table, t=60, fc = 16)  6% interest 
  
  	find u
  	    n = 60-24 = 36
  	    P = 232
  	    V = (find 6% and 36 in the table) 9.52
  
              u = n*P*V/(100+V)
  	    u = 36*232*9.52/(100+9.52) = 726
  
  	He still needs to pay
  	    232*36-726 = 7,626
  	Plus he needs to make this payment
  	    7626+232 = 7858