Aims and overview
In this session students will apply algebraic and numerical skills in transforming
formulae and solving equations, including exponential equations, in the context
of simple and compound interest calculations.
– simple interest (flat or fixed rate), compound interest (reducing balance or
effective rate), principal, amount, rate of interest, time interval, percentage,
decimal equivalents, percentage of an amount, exponent (or index, logarithm,
or power), base, nth root, laws of exponents.
Students will need scientific calculators for use in Question 5.
– Provide a mini-lesson on the variables and formulas for simple and compound
interest calculations. In particular, review percentage equivalents, for example
r = 5% = 0.05 for simple interest calculations and R = 1 + r = 105% = 1.05 for
use in compound interest calculations. Also indicate how scientific calculators
can be used to write a number as a power of 10.
B: Work period
– Monitor student work in Question 1, in particular, to see which students use
step by step calculations rather than formulas. Promote discussion of their
answers to part d. Encourage ‘same to both sides’ justification of each step
in the algebraic work in Questions 2 to 4.
– Make note of all the different ways in which scientific or simpler calculators
can be used to do the numerical calculations of Questions 4c and 5. Support
students in writing out the steps of the algebraic transformations involved
in Questions 2, 3 and 4.
– Discuss the alternative methods for finding solutions and their justifications in
terms of the laws of exponents. Obtain agreement about the eleven formulas
involved in the lesson. Ask students to provide the detail of the algebraic steps
involved in obtaining one or more of these formulas.
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There are two main types of interest; simple interest (or flat or fixed rate interest