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 equationY = 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