{"id":1160,"date":"2020-11-24T17:33:43","date_gmt":"2020-11-24T22:33:43","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/?post_type=back-matter&#038;p=1160"},"modified":"2025-05-21T14:57:31","modified_gmt":"2025-05-21T18:57:31","slug":"formulas","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/back-matter\/formulas\/","title":{"raw":"Formulas","rendered":"Formulas"},"content":{"raw":"<h2>Chapter 1: Mathematics of Merchandising<\/h2>\r\nProfit\u00a0 = Sales \u2013 Costs\r\n\r\n[latex]\\text{Gross Profit} = Sales - \\text{Cost of Goods Sold} = Sales - COGS[\/latex]\r\n\r\n[latex]\\text{Net Profit} = Sales - \\text{Total Costs} = GP - \\text{Operating Expenses}[\/latex]\r\n\r\n[latex]\\text{Percent Markup} = \\frac{Profit}{Cost}[\/latex]\r\n\r\n[latex]\\text{Percent Margin} = \\frac{Profit}{Sales}[\/latex]\r\n\r\n[latex]Sales = Cost \\times (1+ \\% Markup)[\/latex]\r\n\r\n[latex]Net = List(1-d_1)(1-d_2)(1-d_3)[\/latex]\r\n<h2>Chapter 2: Functions<\/h2>\r\n[latex]Slope = \\frac{Rise}{Run} = \\frac{y_2-y_1}{x_2-x_1}[\/latex]\r\n\r\n[latex]\\text{Equation of a line: }Y = Intercept + slope \\times X[\/latex]\r\n\r\n[latex]Revenue = price \\times Quantity = price\\times X[\/latex]\r\n\r\n[latex]Costs = \\text{Fixed Costs}-\\text{Variable Costs}\\times Quantity = FC+VC X[\/latex]\r\n\r\n[latex]Profit = Revenue - Costs = price\\times X - FC - VC X = (price- VC)X-FC[\/latex]\r\n\r\n[latex]\\text{Contribution Margin} = price - VC = \\text{markup in dollars for 1 item}[\/latex]\r\n\r\n&nbsp;\r\n<h2>Chapter 3: Simple Interest<\/h2>\r\n[latex]I = Prt[\/latex]\r\n\r\n[latex]FV = P + I = P(1+rt)[\/latex]\r\n\r\n[latex]P = \\frac{FV}{1+rt}[\/latex]\r\n\r\n&nbsp;\r\n<h2>Chapter 4: Compound Interest<\/h2>\r\n[latex]FV = PV(1+i)^n[\/latex]\r\n\r\n[latex] i = \\frac{j_m}{m}[\/latex]\r\n\r\n[latex]PV = \\frac{FV}{(1+i)^n}= FV(1+i)^{-n}[\/latex]\r\n<h2>Chapter 5: Annuities<\/h2>\r\n<h3>Ordinary Perpetuities:<\/h3>\r\n[latex]PMT = PV\\times i[\/latex]\r\n\r\n[latex]PV = \\frac{PMT}{i}[\/latex]\r\n<h3>Perpetuities Due<\/h3>\r\n[latex]PMT_{Due} = \\frac{PV\\times i}{1+i}[\/latex]\r\n\r\n[latex]PV_{Due} = \\frac{PMT}{i}+PMT[\/latex]\r\n\r\nTo switch to payments at the beginning of the interval:\r\n<ul>\r\n \t<li>Press <strong>2ND BGN<\/strong> (above the PMT key). The display should show END.<\/li>\r\n \t<li>Press <strong>2ND SET<\/strong> (above the ENTER key). The display should show BGN.<\/li>\r\n \t<li>Press <strong>CE\/C <\/strong>(bottom left corner) or <strong>2ND QUIT<\/strong> (top left corner).<\/li>\r\n<\/ul>\r\nTo go back to payments at the END of the interval:\r\n<ul>\r\n \t<li>Press <strong>2ND BGN<\/strong> (above the PMT key) The display should show BGN.<\/li>\r\n \t<li>Press <strong>2ND SET<\/strong> (above the ENTER key). The display should show END.<\/li>\r\n \t<li>Press <strong>CE\/C <\/strong>(bottom left corner) or <strong>2ND QUIT<\/strong>\u00a0 (top left corner)<\/li>\r\n<\/ul>\r\n<h3>Extra Annuity Formula (for when you don't have a BAII Plus)<\/h3>\r\n<h5>\u00a0Future Value of an Ordinary Annuity<\/h5>\r\n&nbsp;\r\n<div>[latex]FV = PMT \\cdot \\frac{(1 + i)^n - 1}{i}[\/latex]<\/div>\r\n<div><\/div>\r\n<h5>Present Value of an Ordinary Annuity<\/h5>\r\n&nbsp;\r\n<div>\r\n\r\n[latex]PV = PMT \\cdot \\frac{1 - (1 + i)^{-n}}{i}[\/latex]\r\n\r\n<\/div>\r\n<div><\/div>\r\n<h5>Future Value of an Annuity Due<\/h5>\r\n&nbsp;\r\n<div>[latex]FV_{\\text{due}} = PMT \\cdot \\frac{(1 + i)^n - 1}{i} \\cdot (1 + i)[\/latex]<\/div>\r\n<div><\/div>\r\n<h5>\u00a0Present Value of an Annuity Due<\/h5>\r\n<div><\/div>\r\n[latex]PV_{\\text{due}} = PMT \\cdot \\frac{1 - (1 + i)^{-n}}{i} \\cdot (1 + i)[\/latex]\r\n<div><\/div>\r\n<div><\/div>\r\n<h5>\u00a0Solving for PMT (Periodic Payment) Given Future Value (Ordinary Annuity)<\/h5>\r\n<div><\/div>\r\n<div>[latex]PMT = \\frac{FV \\cdot i}{(1 + i)^n - 1}[\/latex]<\/div>\r\n<div><\/div>\r\n<div><\/div>\r\n<h5>Given Present Value (Ordinary Annuity)<\/h5>\r\n<div><\/div>\r\n<div>[latex]PMT = \\frac{PV \\cdot i}{1 - (1 + i)^{-n}}[\/latex]<\/div>\r\n<div><\/div>\r\n<div><\/div>\r\n<h5>Given Future Value (Annuity Due)<\/h5>\r\n<div><\/div>\r\n<div>[latex]PMT = \\frac{FV \\cdot i}{[(1 + i)^n - 1] \\cdot (1 + i)}[\/latex]<\/div>\r\n<div><\/div>\r\n<div><\/div>\r\n<h5>Given Present Value (Annuity Due)<\/h5>\r\n<div><\/div>\r\n<div>[latex]PMT = \\frac{PV \\cdot i}{[1 - (1 + i)^{-n}] \\cdot (1 + i)}[\/latex]<\/div>\r\n<div><\/div>\r\n&nbsp;\r\n<h2>Chapter 6: Investment Decisions<\/h2>\r\n&nbsp;","rendered":"<h2>Chapter 1: Mathematics of Merchandising<\/h2>\n<p>Profit\u00a0 = Sales \u2013 Costs<\/p>\n<p>[latex]\\text{Gross Profit} = Sales - \\text{Cost of Goods Sold} = Sales - COGS[\/latex]<\/p>\n<p>[latex]\\text{Net Profit} = Sales - \\text{Total Costs} = GP - \\text{Operating Expenses}[\/latex]<\/p>\n<p>[latex]\\text{Percent Markup} = \\frac{Profit}{Cost}[\/latex]<\/p>\n<p>[latex]\\text{Percent Margin} = \\frac{Profit}{Sales}[\/latex]<\/p>\n<p>[latex]Sales = Cost \\times (1+ \\% Markup)[\/latex]<\/p>\n<p>[latex]Net = List(1-d_1)(1-d_2)(1-d_3)[\/latex]<\/p>\n<h2>Chapter 2: Functions<\/h2>\n<p>[latex]Slope = \\frac{Rise}{Run} = \\frac{y_2-y_1}{x_2-x_1}[\/latex]<\/p>\n<p>[latex]\\text{Equation of a line: }Y = Intercept + slope \\times X[\/latex]<\/p>\n<p>[latex]Revenue = price \\times Quantity = price\\times X[\/latex]<\/p>\n<p>[latex]Costs = \\text{Fixed Costs}-\\text{Variable Costs}\\times Quantity = FC+VC X[\/latex]<\/p>\n<p>[latex]Profit = Revenue - Costs = price\\times X - FC - VC X = (price- VC)X-FC[\/latex]<\/p>\n<p>[latex]\\text{Contribution Margin} = price - VC = \\text{markup in dollars for 1 item}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<h2>Chapter 3: Simple Interest<\/h2>\n<p>[latex]I = Prt[\/latex]<\/p>\n<p>[latex]FV = P + I = P(1+rt)[\/latex]<\/p>\n<p>[latex]P = \\frac{FV}{1+rt}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<h2>Chapter 4: Compound Interest<\/h2>\n<p>[latex]FV = PV(1+i)^n[\/latex]<\/p>\n<p>[latex]i = \\frac{j_m}{m}[\/latex]<\/p>\n<p>[latex]PV = \\frac{FV}{(1+i)^n}= FV(1+i)^{-n}[\/latex]<\/p>\n<h2>Chapter 5: Annuities<\/h2>\n<h3>Ordinary Perpetuities:<\/h3>\n<p>[latex]PMT = PV\\times i[\/latex]<\/p>\n<p>[latex]PV = \\frac{PMT}{i}[\/latex]<\/p>\n<h3>Perpetuities Due<\/h3>\n<p>[latex]PMT_{Due} = \\frac{PV\\times i}{1+i}[\/latex]<\/p>\n<p>[latex]PV_{Due} = \\frac{PMT}{i}+PMT[\/latex]<\/p>\n<p>To switch to payments at the beginning of the interval:<\/p>\n<ul>\n<li>Press <strong>2ND BGN<\/strong> (above the PMT key). The display should show END.<\/li>\n<li>Press <strong>2ND SET<\/strong> (above the ENTER key). The display should show BGN.<\/li>\n<li>Press <strong>CE\/C <\/strong>(bottom left corner) or <strong>2ND QUIT<\/strong> (top left corner).<\/li>\n<\/ul>\n<p>To go back to payments at the END of the interval:<\/p>\n<ul>\n<li>Press <strong>2ND BGN<\/strong> (above the PMT key) The display should show BGN.<\/li>\n<li>Press <strong>2ND SET<\/strong> (above the ENTER key). The display should show END.<\/li>\n<li>Press <strong>CE\/C <\/strong>(bottom left corner) or <strong>2ND QUIT<\/strong>\u00a0 (top left corner)<\/li>\n<\/ul>\n<h3>Extra Annuity Formula (for when you don&#8217;t have a BAII Plus)<\/h3>\n<h5>\u00a0Future Value of an Ordinary Annuity<\/h5>\n<p>&nbsp;<\/p>\n<div>[latex]FV = PMT \\cdot \\frac{(1 + i)^n - 1}{i}[\/latex]<\/div>\n<div><\/div>\n<h5>Present Value of an Ordinary Annuity<\/h5>\n<p>&nbsp;<\/p>\n<div>\n<p>[latex]PV = PMT \\cdot \\frac{1 - (1 + i)^{-n}}{i}[\/latex]<\/p>\n<\/div>\n<div><\/div>\n<h5>Future Value of an Annuity Due<\/h5>\n<p>&nbsp;<\/p>\n<div>[latex]FV_{\\text{due}} = PMT \\cdot \\frac{(1 + i)^n - 1}{i} \\cdot (1 + i)[\/latex]<\/div>\n<div><\/div>\n<h5>\u00a0Present Value of an Annuity Due<\/h5>\n<div><\/div>\n<p>[latex]PV_{\\text{due}} = PMT \\cdot \\frac{1 - (1 + i)^{-n}}{i} \\cdot (1 + i)[\/latex]<\/p>\n<div><\/div>\n<div><\/div>\n<h5>\u00a0Solving for PMT (Periodic Payment) Given Future Value (Ordinary Annuity)<\/h5>\n<div><\/div>\n<div>[latex]PMT = \\frac{FV \\cdot i}{(1 + i)^n - 1}[\/latex]<\/div>\n<div><\/div>\n<div><\/div>\n<h5>Given Present Value (Ordinary Annuity)<\/h5>\n<div><\/div>\n<div>[latex]PMT = \\frac{PV \\cdot i}{1 - (1 + i)^{-n}}[\/latex]<\/div>\n<div><\/div>\n<div><\/div>\n<h5>Given Future Value (Annuity Due)<\/h5>\n<div><\/div>\n<div>[latex]PMT = \\frac{FV \\cdot i}{[(1 + i)^n - 1] \\cdot (1 + i)}[\/latex]<\/div>\n<div><\/div>\n<div><\/div>\n<h5>Given Present Value (Annuity Due)<\/h5>\n<div><\/div>\n<div>[latex]PMT = \\frac{PV \\cdot i}{[1 - (1 + i)^{-n}] \\cdot (1 + i)}[\/latex]<\/div>\n<div><\/div>\n<p>&nbsp;<\/p>\n<h2>Chapter 6: Investment Decisions<\/h2>\n<p>&nbsp;<\/p>\n","protected":false},"author":883,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"back-matter-type":[],"contributor":[],"license":[],"class_list":["post-1160","back-matter","type-back-matter","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/back-matter\/1160","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/users\/883"}],"version-history":[{"count":14,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/back-matter\/1160\/revisions"}],"predecessor-version":[{"id":4009,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/back-matter\/1160\/revisions\/4009"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/back-matter\/1160\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/media?parent=1160"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/back-matter-type?post=1160"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/contributor?post=1160"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/license?post=1160"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}