College Math

Where, = Effective interest rate r = Nominal interest rate n = Number of compounding periods per year Let us solve an example to understand the application of this concept. Suppose, we need to find the effective rate of 9% interest compounded monthly. Here, r = 0.09 and m = 12 (since there are 12 months in a year). Substituting the values in the above formula, we get: = �1 + 0.09 12 � 12 − 1 = 0.0938 9.38% 2.10 Effective Annual Yield/Annual Percentage Rate (APR) Annual percentage rate or effective annual yield are generally calculated when we have to compare a variety of financing or investment options. It is used to evaluate the effective cost you pay on loans every year. You would like to select the financing option that charges the lowest annual percentage rate. In simple words, it calculates the rate of interest that you pay every year, inclusive of the amount of interest. APR is calculated using the following formula: = (1 + ) C = Amount of loan A = Amount of single repayment done after n years i = APR n = Number of years after which the repayment is made For instance, suppose you takes a loan from bank for $2000 and agree to pay back $2500 at the end of three years. What is the APR of the transaction? Applying the formula given above, C = 2000, A = 2500, n = 3

Achieve 2000 = 2500 (1 + ) 3 (1 + ) 3 = 2500 2000

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