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Interest Simple Interest

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									                                     Chapter 7
                                   Simple Interest
Lecture Outline

7.1   Simple Interest
      A.    Definition of “Interest”
      B.    Simple Interest Formulas: I = P × R × T and M = P(1 + RT)

7.2   Solving for Principal, P; Rate, R; and Time, T

7.3   Exact Interest and Ordinary Interest
      A.    Definition of Exact Interest, 365 days per year
      B.    Definition of Ordinary Interest, 360 days per year, and 30 days per month
      C.    Review of Methods For Determining the Exact Number of Days in a Period

7.4   Future Value and Present Value of Simple Interest
      A.    Time value of money
      B.    Future value = Fv = M = P + I = P(1 + RT)
      C.    Present value = Pv =
                                 (1 + RT)

Teaching Comments

A.    General Suggestions
      1.   Encourage the students to write down the formulas and steps necessary to solve each
           problem. Encourage them to make a mental estimate (approximation) of the answer.
           Then have them calculate the answer on their calculator.
      2.   We recommend that students solve the equations I = PRT, M = P(1 + RT) and for any of
           the variables by using algebraic techniques, rather than by the memorization of a
           formula. However, we have included the triangle device for use if that is deemed best
           for students.
      3.   The concept of time value of money is first introduced here to give the student a basic
           understanding of that concept. Present value is especially challenging since the phrase
           “present value” is generally accepted to mean the principal that must be invested at some
           point to generate a specific future value. However, we also can speak of the value of an
           investment at some time within the overall term of the investment. That is what is its
           value presently, which is often phrased as present value of the investment. This early
           introduction will provide an opportunity to explore the meaning of the words with

           students and then set up a means to solve the problem.

B.   Teaching Notes
     7.1 Simple Interest
          a.    Interest is a sum of money paid or charged for the use of money.
          b.    Interest = principal × rate × time
                I = PRT
          c.    Maturity value of simple interest equals principal plus interest.
                M = P + I = P + PRT = P(1 + RT)

     7.2   Solving for Principal, Rate, and Time
           a.    As mentioned above, teach the student to solve the equation I = P × R × T for P,
                 R, and T algebraically.
                 I = PRT                     I = PRT                     I = PRT
                       I                           I                           I
                 P=                          R=                          T=
                      RT                          PT                          PR

     7.3   Exact and Ordinary Interest
           a.    Ordinary interest is the simple interest determined by assuming each month has 30
                 days and that there are 360 days in a year. The simple interest time is determined
                 by dividing the number of days by 360.
           b.    Exact interest assumes that there are 365 days in a year and simple interest time is
                 determined by dividing the number of days by 365.
           c.    Days of the month and days in a year methods for calculating “number of days”
                 and “due date” explanations occur in Chapter 5 section 3.

     7.4   Future Value and Present Value
           a.   Time value of money indicates that as time passes the value of money invested
                may change. The value of an investment can be calculated at any time during the
                term of the investment, as well as at the beginning and end of the investment term.
           b.   Future value is the value of an investment at the end of the investment time frame.
           c.   Present value is the amount of money that must be invested at any particular time
                so that the investment will grow to be a specific future value at some time in the
                future. This phrase is sometimes used to inquire about the value of an investment
                at the present time (i.e., presently). The context of the sentence is very important
                when trying to solve problems using the phrase “present value”.
           d.   Interest earned when the future value and original principal invested are known is
                I = Fv − P.
           e.   Finance charge is the amount of interest paid for a loan.
           f.   A sinking fund is an investment fund created to pay off a future purchase.

g.   Future value of a simple interest investment is the maturity value.
     Fv = M = P(1 + RT)
h.   Present value of an investment is the amount that must be invested presently in
     order to have a specific amount in the future.
                                                      Maturity value
     Present value of a simple interest investment =
                                                         (1 + RT)
     Pv = M(1 + RT)


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