Simple Interest

Discussion

• There are many ways to borrow money.
• The easiest to work with is a simple interest loan
• The principal is the amount of money borrowed.
• The interest is money paid for the use of the principal
• The borrower must repay both the principal and the interest
• All loans are for a fixed period of time.
• The interest rate is a percentage used to calculate interest due.
• Interest rates are often stated in terms of years, or annual rate
• Both the time and the interest rate must be in the same units.
• Simple interest is calculated

   interest = principal × rate × time
      i = prt
      

• Example 1

  p = $450
  r = 5.5%
  t = 2 years
  
      i = prt
      i = 450×.055×2 = $49.5
      

• Example 2

  p = $365.45
  r = 11 1/2 %
  t = 8 months
  
       8 months = 8/12 year  = 2/3 year
  
       i = prt
       i = 365.45 × .115  × 2/3 = $28.02
      

• Example 3:

  p = $550.31
  r = 8.9%
  t = 67 days  (we are told to assume 1 year = 360 days)
  
       67 days = 67/360 years
  
       i = prt
       i = 550.31 × .089 × 67/360 = $9.12
      

• Given any three, we can find the fourth.
• Example 4:

  p = ?
  r = 3%
  t = 90 days
  i = $600
  
        90 days = 90/360 years
  
        i = prt
       --   ---
       rt    rt
  
        p = i/rt
        p = 600/(90/360×0.03)  = 600/0.0075 = $80,000
      

• A discount note requires the borrower to pay the interest in advance.
• This interest is called the bank discount
• The borrower receives both the principal and the interest.
• The discount rate is not the same as the annual percentage rate.
• Example 5:

   (Number 28, page 610)
  p = $2500
  r = 8%
  t = 5 months
  
       Calculate the interest:
  
       i = prt
       i = 2500 × .08 × 5/12 = $83.33
  
       So the amount borrowed was
       2500-83.33 = $2,416.67
  
       And the apr is
       i = prt
       r = i/pt
  
       r = 83.33/(2,416.67*5/12) = 83.33/ = .00827 = 8.3% 
      

Homework