1.5 Use of Data and Graphs

Constructing Graphs from Tables

  • Given a table containing the x and y values of several points on a graph, we can construct a graph by plotting the known points and draw between them, using the trend of points to guess the overall shape of the graph.
  • When guessing the shape of the graph, there are many possible options. It is best to go with the simplest option.

Example

X

Y

0.5

11

1

8.5

1.5

5.5

2

4

3

2

4.5

1.8

6

1.2

9

1

We wish to construct a graph from the above table. To begin, we plot the points on a graph:

Picture 2

Now, we draw between these points. In this case, the overall trend appears to curve and so we will draw a curved line:

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4.2 Modelling Compound Interest Systems with Regular Withdrawals using Tables

Note: if you cannot remember how to model reducing balance systems with regular repayments, revise notes for 4.1 Modelling Compound Interest Systems with Regular Withdrawals.

Guidelines to using a Table for Compound Interest Systems with Regular Withdrawals

  • Tables provide a convenient method for analysing compound interest systems with regular withdrawals, especially when there are regular systemic changes (e.g. the interest rate or withdrawals change regularly).
  • The columns of the table should list, the compounding period, withdrawal, interest earned, principal addition (i.e. the amount the system has increased/decreased during each compounding period) and the balance at the end of the compounding period.
  • The principal addition can be calculated as follows:
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3.2 Modelling Reducing Balance Systems with Regular Repayments using Tables

Note: if you cannot remember how to model reducing balance systems with regular repayments, revise notes for 3.1 Modelling Reducing Balance Systems with Regular Repayments.

Guidelines to using a Table for Reducing Balance Systems

  • Tables provide a convenient method for analysing reducing balance systems, especially when there are regular systemic changes (e.g. the interest rate or repayments change regularly).
  • The columns of the table should list, the compounding period, payment, interest charged, principal addition (i.e. the amount the system has increased/decreased during each compounding period) and the balance at the end of the compounding period.
  • The principal addition can be calculated by as follows:
Read More »3.2 Modelling Reducing Balance Systems with Regular Repayments using Tables