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An interest rate takes two forms: nominal interest rate and effective interest rate. The nominal interest rate does not take into account the compounding period. The effective interest rate does take the compounding period into account and thus is a more accurate measure of interest charges. A statement that the "interest rate is 10%" means that interest is 10% per year, compounded annually. In this case, the nominal annual interest rate is 10%, and the effective annual interest rate is also 10%. However, if compounding is more frequent than once per year, then the effective interest rate will be greater than 10%. The more often compounding occurs, the higher the effective interest rate. The relationship between nominal annual and effective annual interest rates is: ia = [ 1 + (r / m) ] m - 1 where "ia" is the effective annual interest rate, "r" is the nominal annual interest rate, and "m" is the number of compounding periods per year. Example: A credit card company charges 21% interest per year, compounded monthly. What effective annual interest rate does the company charge? r = 0.21 per year m = 12 months per year ia = [ 1 + (.21 / 12) ] 12 - 1 = [1 + 0.0175 ] 12 - 1 = (1.0175)12 - 1 = 1.2314 - 1 = 0.2314 = 23.14% It may be desired to find the effective interest rate for a period other than annual. In this case, adjust the period for "r" and "m" as needed. For example, if the effective interest rate per semi annual period (every 6 months) is desired, then r = nominal interest rate per 6 months m = number of compounding periods per 6 months and the effective interest rate, isa, per semi-annual period, is: isa = [ 1 + (r / m) ] m - 1 More Interest FormulasNominal and Effective Interest RatesQuestion 1 Question 2 Return to Nominal and Effective Interest Rate Return to Interest Formulas Tutorials menu Return to Tutorials menu Question 1. If a lender charges 12% interest, compounded quarterly, what effective annual interest rate is the lender charging? Choose an answer by clicking on one of the letters below, or click on "Review topic" if needed. A ia = [ 1 + (0.12 / 12) ] 12 - 1 = (1.01)12 - 1 = 1.1268 - 1 = .1268 = 12.68% B ia = [ 1 + 0.12 ] 12 - 1 = (1.12)12 - 1 = 3.8960 - 1 = 2.8960 = 289.6% C ia = [ 1 + (0.12 / 12) ] 4 - 1 = (1.01)4 - 1 = 1.0406 - 1 = .0406 = 4.06% D ia = [ 1 + (0.12 / 4) ] 4 - 1 = (1.03)4 - 1 = 1.1255 - 1 = .1255 = 12.55% Review topic Question 2. If a lender charges 12% interest, compounded monthly, what is the effective interest rate per quarter? Hint: m = number of compounding periods per quarter Let i = effective interest rate per quarter. Choose an answer by clicking on one of the letters below, or click on "Review topic" if needed. A i = [ 1 + (0.12 / 3) ] 3 - 1 = (1.04)3 - 1 = 0.1249 = 12.49% B i = [ 1 + 0.03 ] 12 - 1 = (1.03)12 - 1 = 0.4258 = 42.58% C i = [ 1 + (0.03 / 3) ] 3 - 1 = (1.01)3 - 1 = 0.0303 = 3.03% D i = [ 1 + (0.03 / 12) ] 3 - 1 = (1.0025)3 - 1 = 0.0075 = 0.75% Review topic Find the nominal rate compounded monthly which is equivalent to 12% compounded quarterly. What is the corresponding effective rate? Expert Solution  Students who’ve seen this question also like: Related Finance Q&AFind answers to questions asked by students like you. Q: An interest of 8% compounded semi annually is how many percent if compounded quarterly? A: Formula: Effective interest rate=1+rnn-1where,r=nominal raten=number of compounding periods in a… Q: nd the nominal rate which if converted semi - annually could be used instead of 12% compounded bi -… A: In this we have to find out the effective rate for both options and than find equivalent rate. 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What nominal rate is equal to effective rate of 12% compounded monthly?The nominal interest rate is the periodic interest rate times the number of periods per year. For example, a nominal annual interest rate of 12% based on monthly compounding means a 1% interest rate per month (compounded).
What effective rate is equivalent to a nominal rate of 12 compounded quarterly?Answer and Explanation:
The correct answer is c) 12.55%.
What is 12% interest compounded monthly?"12% interest compounded monthly" means that the interest rate is 12% per year (not 12% per month), compounded monthly. Thus, the interest rate is 1% (12% / 12) per month.
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What nominal rate compounded monthly is equivalent to 12 compounded quarterly?
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