Installment Buying

Discussion

• This is the normal type of loan you think of (car, ...)
• You take money and then each month you pay a bit back.
• Open ended loans, like credit cards, you pay a variable amount depending on how much you spent.
• Fixed loans you pay a fixed amount each month.

Fixed Loans

• A loan is for a fixed period at a fixed interest rate.
• Using the chart on page 623, compute the finance charge
  • In their example 7% for 24 months is 7.54, circled in red
  • 7.5% for 48 months is 16.06, circled in green
• This is the charge per $100
• Next find how many $100 you are borrowing (divide principal/100)
• Multiply finance charge per $100 by the number of $100
• This is the total finance charge.
• Example 1

       Compute the finance charges  for a $5,000 for 30 months at 8.0% interest
  
       Look up 30,8 in the chart -> 10.66
       Compute the number of 100 in 5,000
           5000/100 = 50
       Compute the finance charge    10.66 × 50 = 533
       

• From this we can compute the total price of the loan, and the monthly payments.
• Example 1, cont

  Total price = principal + finance charges
              = 5000 + 533
  	    = $5533
  Monthly payment =  total price / months to pay
              = 5533 / 50 = 110.66
       

• Example 2, Problem 14, page 631

      Price of computer $1495
      Down 5%  ( 1495 x 0.05 = 74.75)
      Amount Financed = 1495-74.75 = 1420.25
      Payment $64 per month
      Period = 24 months
  
      Total price of loan 64× 24 =  $1536
      Finance Charges = 1536 - 1420.25 = 115.75
  
      What was the APR?
  
           hundreds financed = 14.2
  	 Finance charges 115.75
  
  	 Finance charge / 100 = 115.75/14.2 = 8.15
  	 Look this up in the chart - look along the 24 line (8.0) in 7.5%
     

• If you want to pay a loan off early, you use one of the two formulas on the top of page 625.
• The Actuarial method

           n P V                u = unearned interest
     u =  ------                n = remaining payments
          100 + V               P = monthly payment
  	                      V = value from APR table
  

• Example 3, problem 18 page 361

  time = 48 months
  Monthly payment = 167.67
  Principal = 7500
  Payment 18
  
  Total Payment = 167.67 x 48 = 8048.16
  Finance Charge = 8048.16 - 7500 = 548.16
  Hundreds financed = 75
  Charge/100  = 548.16/75 = 7.3
  APY = Look this up in the chart =  3.5%
  n = 48 - 18 = 30 
  P = 167.67
  V = 4.58  (look this up based on N and APY 
  
             30 * 167.67 *4.58 
    u =      -----------------   =  220.29
               100 + 4.58 
  
  The remaining balance to be paid is 30x 167.67 = 5030.10
  But this includes the extra finance charge 220.29
  So the payoff is 5030.10 - 220.29 = 4809.81
      

Homework