Simple Interest

• We frequently borrow money in this world.
• A Simple Interest Loan is the simplest type of loan.
  • You borrow a fixed amount of money, the Principal , p
  • For a given amount of time, t
  • At a fixed rate of interest or rate, r
  • At the end of the period you must repay both the principal
  • And interest or rent to use the money.
  • This is modeled by the formula i = prt
• Not many places will do simple interest loans
• But it is the foundation for many other types of loans.
• Example: Problem 9, page 618

  p = $300, r = 1.5%, t = 4 years
  
  i = prt
  i = 300 x 0.015 x 5 
    = $18
      

• Example: Problem 19 page 618

  p = $1500,   r = ?  t = 4 years, i = $336.00
  
  i = prt, divide through by pt 
  i/pt =r 
  
  336/(4*1500) = r
    r = 0.056
      = 5.6%
  

• Caution
  • Time and rate must both be in the same units.
  • Unless otherwise stated, interest is given in terms of years
  • A month has 30 days and a year has 360 days.
• Problem 11 page 618

  p = $1,100, r = 8.75%, t = 90 days.
  
  In this case, 90days x 1 year/360 days = 1/4 year.  
  So  t = 1/4
  
  i = prt
  i = 1100 x 0.875 x 1/4 
    = 24.0625
    = $24.06
      

• Problem 25 page 618

  Josh uses the SBA loan program to obtain a loan to help expand his business.  Josh borrows $25,000 for 2 years with simple interest of 1.5%.  Determine the amount Josh must repay after 2 years.
  
  r = 1.5%
  p = $25,000
  t = 2
  
  i = prt 
  i = $25000x0.015x2
    = $750
  
  But we were not ask for interest, we were ask for the amount he must repay
  A = i + p
  A = $750 + $25,000
    = $25,750
      

• A Discount Note is a simple interest loan with a twist
  • The borrower needs to repay the amount listed on the note, this is both principal and interest.
  • This type of problem will contain the word discount with respect to the loan or the interest rate.
  • Just remember "You need to work this twice"
  • The question will probably also ask for the "actual rate of interest"
• 28 page 619

  Kwame borrowed $2500 for 5 months from a bank using U.S. Government bonds as security.  The bank discounted the loan at 2%.
  
  a. How much interest did Kwame pay 
  b. How much did he receive from the bank?
  c. What was the actual rate of interest.
  
  a.  i = prt    p = $2,500, r = 2%, t = 5 months, or 5/12 year.
      i = 2500x0.02x5/12
        = 20.83
  
  b. A = p + i
     2500 = p + 20.83
     2500-28.83 = p
     p = 2,479.17
  
  c i = prt   i = 20.83, p = 2,479.17, r = x t = 5/12
    r = i/pt
    r = 20.83/(2479.17x5/12)
    r = 0.02016
      = 2.02%