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Understanding Nominal and Effective Interest Rates Equation

Learn how nominal rates are converted into effective rates using the equation i = (1 + r/m)^m – 1. Calculate rates for different time periods like quarterly or yearly with examples.

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Understanding Nominal and Effective Interest Rates Equation

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  1. Nominal rates can be converted into effective rates via the following equation: i = (1 + r / m)m – 1 Where : i = effective interest rate for any time period r = nominal rate for same time period as i m = no. times interest is comp’d in period specified for i Example: For an interest rate of 1.2% per month, determine the nominal and effective rates (a) per quarter, and (b) per year Effective Interest Calculations Solution: (a) Nominal r / quarter = (1.2)(3) = 3.6% per quarter Effective i / quarter = ( 1 + 0.036/ 3)3 – 1 = 3.64% per quarter (b) Nominal i /yr = (1.2)(12) = 14.4% per year Effective i / yr = (1 + 0.144 / 12)12 – 1 = 15.39% per quarter

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