{"id":463,"date":"2020-04-27T20:10:21","date_gmt":"2020-04-28T00:10:21","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/?post_type=chapter&#038;p=463"},"modified":"2021-06-29T11:42:54","modified_gmt":"2021-06-29T15:42:54","slug":"nominal-and-periodic-rates","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/chapter\/nominal-and-periodic-rates\/","title":{"raw":"4.2 Nominal and Periodic Rates","rendered":"4.2 Nominal and Periodic Rates"},"content":{"raw":"<div>\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Key Takeaways<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\"><em>[pb_glossary id=\"468\"]Nominal rate[\/pb_glossary]: Percent annual rate; \u00a0[pb_glossary id=\"469\"]Periodic rate[\/pb_glossary]: Rate that gives percent interest each period.<\/em><\/div>\r\n<\/div>\r\n&nbsp;\r\n\r\n<\/div>\r\nWhen compound-interest rates are given as above, the percent annual rate is called the <em>nominal rate <\/em>and denoted by <em>j. <\/em>To show clearly what the compounding interval is, add a subscript \u00a0to the<em> j<\/em> (<em>j<sub>m<\/sub><\/em>) . This indicates the <em>number of times per year <\/em>the interest is to be compounded.\r\n<ul>\r\n \t<li>Thus, 8% compounded semi-annually would be<em> j<sub>2<\/sub><\/em> = 8%,<em> m<\/em>=2.<\/li>\r\n \t<li>Thus, 18% compounded monthly would be <em>j<sub>12<\/sub><\/em> = 18%, <em>m<\/em>=12.<\/li>\r\n<\/ul>\r\nThe periodic rate is used in most BAII Plus calculations.\r\n\r\nThe rate that gives the percent interest each period is called the <em>periodic rate <\/em>and is denoted by <em>i<\/em>. This is the rate <em>actually used <\/em>in most formulas. The following are examples.\r\n<h2>Example 4.2.1<\/h2>\r\n<ol>\r\n \t<li>For 8% compounded semi-annually (<em>j<sub>2<\/sub><\/em> = 8% =0.08), [latex]i = \\frac{0.08}{2} =0.04 =4%\\text{ per half year}[\/latex]<\/li>\r\n \t<li>For 18% compounded monthly (<em>j<sub>12<\/sub><\/em> = 18% =0.18), [latex]i = \\frac{0.18}{12} =0.015=1.5%\\text{ per month}[\/latex]<\/li>\r\n<\/ol>\r\nIn general, to get <em>i<\/em> from <em>j<sub>m<\/sub><\/em>:\r\n<p style=\"text-align: center\">[latex] i = \\frac{j_m}{m}[\/latex]<\/p>\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n<h2>Your Own Notes<\/h2>\r\n<ul>\r\n \t<li>Are there any notes you want to take from this section? Is there anything you'd like to copy and paste below?<\/li>\r\n \t<li>These notes are for you only (they will not be stored anywhere)<\/li>\r\n \t<li>Make sure to download them at the end to use as a reference<\/li>\r\n<\/ul>\r\n[h5p id=\"1\"]","rendered":"<div>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Key Takeaways<\/p>\n<\/header>\n<div class=\"textbox__content\"><em><a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_463_468\">Nominal rate<\/a>: Percent annual rate; \u00a0<a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_463_469\">Periodic rate<\/a>: Rate that gives percent interest each period.<\/em><\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<p>When compound-interest rates are given as above, the percent annual rate is called the <em>nominal rate <\/em>and denoted by <em>j. <\/em>To show clearly what the compounding interval is, add a subscript \u00a0to the<em> j<\/em> (<em>j<sub>m<\/sub><\/em>) . This indicates the <em>number of times per year <\/em>the interest is to be compounded.<\/p>\n<ul>\n<li>Thus, 8% compounded semi-annually would be<em> j<sub>2<\/sub><\/em> = 8%,<em> m<\/em>=2.<\/li>\n<li>Thus, 18% compounded monthly would be <em>j<sub>12<\/sub><\/em> = 18%, <em>m<\/em>=12.<\/li>\n<\/ul>\n<p>The periodic rate is used in most BAII Plus calculations.<\/p>\n<p>The rate that gives the percent interest each period is called the <em>periodic rate <\/em>and is denoted by <em>i<\/em>. This is the rate <em>actually used <\/em>in most formulas. The following are examples.<\/p>\n<h2>Example 4.2.1<\/h2>\n<ol>\n<li>For 8% compounded semi-annually (<em>j<sub>2<\/sub><\/em> = 8% =0.08), [latex]i = \\frac{0.08}{2} =0.04 =4%\\text{ per half year}[\/latex]<\/li>\n<li>For 18% compounded monthly (<em>j<sub>12<\/sub><\/em> = 18% =0.18), [latex]i = \\frac{0.18}{12} =0.015=1.5%\\text{ per month}[\/latex]<\/li>\n<\/ol>\n<p>In general, to get <em>i<\/em> from <em>j<sub>m<\/sub><\/em>:<\/p>\n<p style=\"text-align: center\">[latex]i = \\frac{j_m}{m}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<h2>Your Own Notes<\/h2>\n<ul>\n<li>Are there any notes you want to take from this section? Is there anything you&#8217;d like to copy and paste below?<\/li>\n<li>These notes are for you only (they will not be stored anywhere)<\/li>\n<li>Make sure to download them at the end to use as a reference<\/li>\n<\/ul>\n<div id=\"h5p-1\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-1\" class=\"h5p-iframe\" data-content-id=\"1\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"Key takeaways, notes and comments from this section document tool.\"><\/iframe><\/div>\n<\/div>\n<div class=\"glossary\"><span class=\"screen-reader-text\" id=\"definition\">definition<\/span><template id=\"term_463_468\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_463_468\"><div tabindex=\"-1\"><p>Percent annual rate in compound interest.<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_463_469\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_463_469\"><div tabindex=\"-1\"><p>Periodic Compound interest rate<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><\/div>","protected":false},"author":883,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-463","chapter","type-chapter","status-publish","hentry"],"part":44,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapters\/463","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/users\/883"}],"version-history":[{"count":10,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapters\/463\/revisions"}],"predecessor-version":[{"id":3389,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapters\/463\/revisions\/3389"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/parts\/44"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapters\/463\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/media?parent=463"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapter-type?post=463"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/contributor?post=463"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/license?post=463"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}