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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