Rates
Unit Rate
• A rate is a comparison of two quantities with
different units
• For instance speed is the rate of displacement
over time or the rate at which distance is covered
in a particular time
• For instance one’s speed could be 230 km every
two hours
• A unit rate is a rate in which the denominator is
one, for instance the previous speed as a unit rate
would be the speed per hour which is 115km/hr
Rates of Change
• When two variables are related such that one is depends
on the other we can say that the first variable is a
dependent variable and the second an independent
variable
• The rate of change of the dependent variable (y) with
respect to the independent (x) variable can be defined as
the change in in y divided by the change in x or ∆y/ ∆x
• This fraction can be expressed as a percentage to obtain
the percentage increase or decrease
• If values of y are plotted against values of x on a Cartesian
graph, this would also be the slope of the graph
Uniform Rates of change
• Therefore assuming uniform change this
would imply a straight line graph
• Therefore any Y can be got from the equation
Y = mX + c where m is the gradient or slope of
the line (∆y/ ∆x) and c is the x intercept or
value of y when x = 0
Interest Rate Problems
• Interest is a charge on a loan or it could be the
earning on a deposit
• This interest can be a simple or compound
interest
• Simple interest is charged or earned on the
original deposit or loan amount also known as
the principle
• With compound interest the principal is
recalculated by adding the simple interest after
each period
Simple Vs Compound Interest
• Given FV is the future value, PV is the present
value, R is the interest rate and T is the time
then
– Simple interest FV = PV + R*T*P
– Compound interest FV = PV(1 + R)^t
• The interest will in both cases would be
– FV - PV