{"id":40069,"date":"2025-10-14T13:54:09","date_gmt":"2025-10-14T13:54:09","guid":{"rendered":"https:\/\/certifeka-edu.com\/programs\/finance-for-strategic-managers-finance-professional-certificate__trashed-2\/lessons\/lesson-7-nominal-and-effective-annual-rates-of-interest-3\/"},"modified":"2025-10-14T13:54:09","modified_gmt":"2025-10-14T13:54:09","slug":"lesson-7-nominal-and-effective-annual-rates-of-interest-3","status":"publish","type":"lesson","link":"https:\/\/certifeka-edu.com\/ar\/programs\/sample-course\/lessons\/lesson-7-nominal-and-effective-annual-rates-of-interest-3\/","title":{"rendered":"Lesson 7: Nominal and effective annual rates of interest"},"content":{"rendered":"
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Lesson 7: Mixed Stream’s Time Value \n<\/h2>\n
Nominal and effective annual rates of interest \n<\/h3>\n
Both businesses and investors need to make objective comparisons of loan costs or investment returns over different compounding periods<\/h5>\n
To put interest rates on a common basis, to allow comparison, we distinguish between nominal and effective annual rates.<\/h5>\n
The nominal, or stated, annual rate is the contractual annual rate of interest charged by a lender or promised by a borrower<\/h5>\n
The effective, or true, annual rate (EAR) is the annual rate of interest actually paid or earned.<\/h5>\n
The effective annual rate reflects the effects of compounding frequency, whereas the nominal annual rate does not.<\/h5>\n
Using the notation introduced earlier, we can calculate the effective annual rate, EAR, by substituting values for the nominal annual rate, r, and the compounding frequency, m, EAR= (1+r\/m)m -1<\/h5>\n
Example<\/h3>\n
Fred Moreno wishes to find the effective annual rate (EAR) associated with an 8% nominal annual rate r = 8%, when interest is compounded (1) annually (m=1) ; (2) semiannually (m= 2) ; and (3) quarterly (m=4) . Substituting these values, we get<\/h5>\n
For Annual compounding: EAR =(1+0.08\/1)1-1 AR=(1+0.08)1 -1 EAR=1+0.08-1 EAR=0.08=8%<\/h5>\n
For Semiannual compounding: EAR =(1+0.08\/2)2-1 EAR=(1+0.04)2 -1 EAR=1.0816-1 EAR=0.0816=8.16%<\/h5>\n
For quarterly compounding: EAR =(1+0.08\/4)4-1 EAR=(1+0.02)4 -1 EAR=1.0824-1 EAR=0.0824=8.24%<\/h5>\n
These values demonstrate two important points:<\/h5>\n
\n
\n
The First is that nominal and effective annual rates are equivalent to annual compounding.<\/h5>\n<\/li>\n<\/ul>\n
\u00a0<\/h5>\n
\n
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The second is that the effective annual rate increases with increasing compounding frequency, up to a limit that occurs with continuous compounding<\/h5>\n<\/li>\n<\/ul>","protected":false},"comment_status":"open","ping_status":"closed","template":"","class_list":["post-40069","lesson","type-lesson","status-publish","hentry"],"yoast_head":"\nLesson 7: Nominal and effective annual rates of interest - Certifeka-edu<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/certifeka-edu.com\/ar\/programs\/sample-course\/lessons\/lesson-7-nominal-and-effective-annual-rates-of-interest-3\/\" \/>\n<meta property=\"og:locale\" content=\"ar_AR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Lesson 7: Nominal and effective annual rates of interest - Certifeka-edu\" \/>\n<meta property=\"og:description\" content=\"Lesson 7: Mixed Stream’s Time Value Nominal and effective annual rates of interest Both businesses and investors need to make objective comparisons of loan costs or investment returns over different compounding periods To put interest rates on a common basis, to allow comparison, we distinguish between nominal and effective annual rates. 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