Simple Interest

• (p) Principal is the amount of money you want to borrow.
• (r) Interest rate is Usually given in terms of years (or annually)
• (i) Interest is the amount of money you owe as "rent" on the principal
• (t) Time is the amount of time the loan is for, should be in the same terms as the interest rate (years/years or months/months)
• i = prt
• This is called simple interest.
• Example: 2, page 419

  P = 7000
  r = 5%
  t = 1 year.
  
  i = prt
  i = 7000 × .05 × 1
  i = 350
     

• Example 6, page 419

  p = 18,000
  r = 7.5%
  t = 18 months
  
  18 months × 1 year / 12 months = 1.5 year
  
  i = 18,000 × .075 × 1.5
  i = 2025
     

• We can do algebra, so 9-20 are not a problem.
• Future Value - principal plus interest.
• A = P(1+rt)
  • A is the total amount
• Example 22

  A = 8500
  r = 7%
  t = 3
  
  A = P(1+rt)
  
  P = A/(1+rt)
  
  P = 8500/(1+.07×3)
    = 8500/1.21
    = 7024.79
     

• For a discount loan the principal and interest are built in.
• For example, I purchase a $25 savings bond for 18.24.
• Example 28, page 420

  p = 3000
  t = 9 months
  r = 8%.
  
  9 months × 1 year /12 months =  .75 years
  
  i =  prt 
  i =  3000 × .75 × .08
  i = 180, this is the discount rate.
  You actually receive 3000 - 180 = 2820.
  
  The interest rate is
     r = i/pt
       = 180/(2820*.75)
       = 8.5%
     

Homework