Installment Buying Part 1

• Installment buying is a type of loan where the principal and and interest are paid off in regular installments.
• If, like most loans, the monthly amount is set, it is a fixed installment loan
• Credit Cards, on the other hand are open installment loans
• We will focus on fixed installment loans for now.
• Normally, when obtaining a loan, you must provide a down payment
  • This is usually a percentage of the purchase price.
  • It reduces the amount of money you will borrow.
• The amount financed = purchase price - down payment.
• Example: When purchasing a used truck for $13,999, Bob is required to put a down payment of 15%. Find the amount of the down payment and the amount financed.

  Down payment = $13,999 x .15 = $2,099.85
  Amount financed = $13,999 - $2099.85  = $11,899.15
     

• The total installment price = total of all monthly payments + down payment
• The finance charge = total installment price - purchase price
• Example:

  Problem 2, Page 488
  
  Purchase Price = $2,450
  Down Payment = $550
  Payments = $94.50
  Number of Payments = 24
  
  Find:
  Amount financed = Purchase price - down payment
                  = $2,450 - $550 = $1,900
  Total installment price = total of all monthly payments + down
              = 24 months x $94.50/month + $550 = $2,818.00
  Finance Charge = Total Installment Price - Purchase Price
              = $2,818 - $2,450  = $368
     

• Table 8.5 page 482 shows the relationship between APR, finance charge/$100 and months paid.
  • You will need to know how to use this table
  • I will give you a copy on the next test and for the final.
  • Given any two, we can find the third
  • Example

    Number 6.
        Months = 18
        Finance Charge / $100 = 12.72
        Find the APR:
    
        APR = 15.5%
           

  • APR is the annual percentage rate for the loan.
  • Months paid is self evident.
  • Finance charge per $100
    • To find the finance charge per $100 given the finance charge
      • Divide the finance charge by the number of hundreds borrowed.
      • This is the formula he gives in the book.
      • example

        Problem 10
        Amount Financed = $1,200
        Months = 30
        Finance Charge = $264
        Find APR
        
        Finance Charge/$100 = 264/(1,200/100) = 264/12 = 22
        Look this up in the chart.
        APR = 16%
        		

    • Given the finance charge/$100
      • Find the number of $100 financed
      • Multiply the two.
      • Example:

        Sue borrows $5,122 for 18 months at 12% APR.  Find the finance charge.
        1. Look up the Finance charge per $100, FC/$100 = $9.22
        2. Compute the number of hundreds borrowed = 5,122/100 = 51.22
        3. Compute the Finance Charge = 9.22 x 51.22 = 472.25
                        

  • Example

    Problem 12
        Purchase Price = $18,000
        Down Payment = $600
        Monthly Payment = $385
        Months = 60
    
    a. Find the amount financed = $18,000 - $600
                                = $17,400
    b. Find the installment price:
             385x60 + 600 =  23,700
    c. Find the finance charge
             23,700 - 1800 = 5,700
    d. Find the APR of the loan
        1. Number of $100 = 17,400/100 =  174
        2. finance charge/$100  = 5,700/174 = 32.75
        3. Look this up in the table.  11.75%
    

• There are two formulas that can be used if you want to pay the loan off early.
  • These are the Actuarial method and the rule of 78
  • Both are ways to estimate the amount of unearned interest (or the interest you don't have to pay)
  • They are only used if you pay a loan off early
  • The rule of 78 is an estimation technique that favors the bank.
  • You pay a penalty for paying the loan off early.
  • Both formulas are given on page 483.

Homework