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