Simple Interest Loans

• Simple interest loans involve
  • Receiving a principal amount (p) from a lender
  • Agreeing to repay that loan in a given amount of time (t)
  • Agreeing to pay rent on the principal, or interest (i)
  • Agreeing to pay a given interest rate (r).
• The formula i=prt gives the relationship between principal, rate, time and interest.
  • Be careful, rate and time must be in the same units.
  • Rate, unless stated otherwise, is given in terms of an annual rate.
  • So turn the time into years, if it is not.
  • In general, we assume a year has 360 days in it.
  • We commonly assume a month has 30 days in it.
• At the end of the loan period, the borrower must return the principal plus the interest to the lender.
• Some examples:
  • p = 400, r = 14%, t = 5 years, find i

    i = prt
    i = 400 × .14 × 5 
      = $280
        

  • p = 400, r = 8.5%, t = 30 days

    The time is not in terms of years, so 
    t = 30 days x 1 year/360 days = 30/360 or 1/12 year
    
    i = prt
    i = 400 X .085 x 1/12
      = 2.8333333
      = $2.83
        

  • p = 697 r = 0.053% daily, t = 9 months.

    The interest rate is not in terms of years
    0.00053/day x 360 days/year = .19 or 19% per year.
    The time is not in terms of years 
    9 months x 1 year/12 months = 3/4 year
    
    i = prt
      = 697 x .19 x 3/4
      = $99.74
        

  • p = 4,200, t = 4 years, i = 700

    i = prt
    r =  i/pt
      =   700/(4200x4)
      = .04166666
      = 4.17%
        

  • i = 108, t = 9 months, r = 8%, p = ?

    The time is not in terms of years
    9 months x 1 year/12 months = 3/4 year
    i = prt
    p = i/rt
      = 108/(.08 x 3/4)
      = 1,800
        

  • (book number 26, page 665) Steve and Laurie borrowed $4500 from their credit union to remodel their kitchen. The simple interest rate was 4.75% and the length of the loan was 3 years.
    1. How much did they pay for the use of the money?
    2. Determine the amount they had to repay to the credit union at the end of the loan.

    i = prt
    p = 4500, r = 4.75%, t = 3 years
    i = 4500 x .0457 x 3 
      = 641.25  (a)
    A = p+i
      = 4500 + 641.75 
      = 5,141.25
        

  • A discount loan is a simple interest loan where the interest is paid in advance.
  • Computations on a discount loan
    • Calculate the interest using i=art
    • Find the actual principal p= a-i
    • Find the APY for the loan r = i/pt
  • Example (number 29, page 66) Julie borrowed $3650 from her bank for 8 months. The bank discounted the loan at 7.5%.
    1. How much interest did Julie pay?
    2. How much did she receive from the bank?
    3. What is the actual rate of interest paid.

    Convert time to years
    8 months x 1 year /12 months = 2/3 year
    i = prt 
    i = 3650 x .075 x 2/3 
      = 182.50
    
    p = a -i
      = 3650 - 182.50 
      = 3,467.50
    
    r = i/pt
      = 182.5/( 3,467.50x2/3)
      = 0.0789
      = 7.9%