{"id":1292,"date":"2026-01-26T17:51:21","date_gmt":"2026-01-26T07:51:21","guid":{"rendered":"https:\/\/archive4ones.com\/2ndstudy\/?p=1292"},"modified":"2026-01-27T12:18:57","modified_gmt":"2026-01-27T02:18:57","slug":"year12-math-1-2-25-investing-and-networking-topic-1","status":"publish","type":"post","link":"https:\/\/archive4ones.com\/2ndstudy\/?p=1292","title":{"rendered":"Year12-math-2-4-2 Investing and Networking (Topic 1)"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><strong>Unit 4<\/strong> of <strong>QLD Year 12<\/strong> General Mathematics (Investing and Networking) focuses on practical financial applications and graph theory. It covers compound interest, loans, annuities, and perpetuity calculations (Topic 1) , alongside network concepts such as graphs, paths, trails, and,Eulerian\/Hamiltonian graphs for modeling decision-making (Topic 2).&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Key Topics in Unit 4: General Mathematics<\/strong>&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Topic 1: Loans, Investments and Annuities<\/strong>\n<ul class=\"wp-block-list\">\n<li><strong>Compound Interest:<\/strong> Calculations, using recurrence relations, and applying the compound interest formula.<\/li>\n\n\n\n<li><strong>Financial Applications:<\/strong> Reducing-balance loans, annuities, and perpetuities.<\/li>\n\n\n\n<li><strong>Rates:<\/strong> Understanding effective annual rates of interest.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Topic 2: Graphs and Networks<\/strong>\n<ul class=\"wp-block-list\">\n<li><strong>Fundamentals:<\/strong> Definitions of vertices, edges, directed graphs (digraphs), and subgraphs.<\/li>\n\n\n\n<li><strong>Matrix Representation:<\/strong> Creating and using adjacency matrices.<\/li>\n\n\n\n<li><strong>Graph Types:<\/strong> Planar graphs and Euler&#8217;s formula (<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>V<\/mi><mo>\u2212<\/mo><mi>E<\/mi><mo>+<\/mo><mi>F<\/mi><mo>=<\/mo><mn>2<\/mn><\/mrow><annotation encoding=\"text\/plain\">cap V minus cap E plus cap F equals 2<\/annotation><\/semantics><\/math>).<\/li>\n\n\n\n<li><strong>Paths and Circuits:<\/strong> Exploring walks, trails, paths, Eulerian graphs, and Hamiltonian graphs.&nbsp;<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">This unit prepares students for real-world financial management and using networks to solve optimization problems.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">********************<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In the Queensland (QLD) Year 12 General Mathematics syllabus,&nbsp;<strong>Graphs and Networks<\/strong>&nbsp;(primarily found in Unit 4) and&nbsp;<strong>Loans, Investments and Annuities<\/strong>&nbsp;(often referred to alongside investing and financial networking) are key components of the curriculum.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Here is a breakdown of the key topics, focusing on the &#8220;Graphs and Networks&#8221; and &#8220;Investing&#8221; aspects:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>1. Loans, Investments and Annuities<\/strong> (Unit 4: Financial Math)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This section involves the &#8220;Investing and Financial Networking&#8221; aspect, focusing on using sequences and recursion to model financial situations.&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Compound Interest:<\/strong>&nbsp;Using recurrence relations to model and solve problems with compound interest investments.<\/li>\n\n\n\n<li><strong>Effective Annual Rate:<\/strong>&nbsp;Calculating the true interest rate per annum.<\/li>\n\n\n\n<li><strong>Reducing-Balance Loans:<\/strong>&nbsp;Using recursion to model loans where interest is calculated on the reducing balance, and determining payment amounts.<\/li>\n\n\n\n<li><strong>Annuities and Perpetuities:<\/strong>&nbsp;Understanding annuities (investments that pay a regular income) and perpetuities.&nbsp;<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">****************************************************************************<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">**********<strong>:<\/strong> <strong>recurrence relations<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In&nbsp;<strong>QLD Year 12 General Mathematics (Unit 4)<\/strong>, a&nbsp;recurrence relation&nbsp;is&nbsp;<mark>a mathematical rule used to model financial situations by defining each term in a sequence based on the value of the preceding term<\/mark>.<mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-base-color\">&nbsp;<\/mark><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>1. Key Financial Models<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Financial applications are categorized into three main types of recurrence relations:&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Simple Interest (Linear Growth\/Decay):<\/strong> Constant amounts are added or subtracted.<br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>V<\/mi><mrow><mi>n<\/mi><mo>+<\/mo><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><msub><mi>V<\/mi><mi>n<\/mi><\/msub><mo>+<\/mo><mi>D<\/mi><\/mrow><annotation encoding=\"text\/plain\">cap V sub n plus 1 end-sub equals cap V sub n plus cap D<\/annotation><\/semantics><\/math><br><em>Where <\/em><math data-latex=\"D=\\frac{r}{100}\\times V_{0}\"><semantics><mrow><mi>D<\/mi><mo>=<\/mo><mfrac><mi>r<\/mi><mn>100<\/mn><\/mfrac><mo>\u00d7<\/mo><msub><mi>V<\/mi><mn>0<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">D=\\frac{r}{100}\\times V_{0}<\/annotation><\/semantics><\/math>.<\/li>\n\n\n\n<li><strong>Compound Interest (Geometric Growth\/Decay):<\/strong> The value is multiplied by a constant factor.<br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>V<\/mi><mrow><mi>n<\/mi><mo>+<\/mo><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mi>R<\/mi><mo>\u00d7<\/mo><msub><mi>V<\/mi><mi>n<\/mi><\/msub><\/mrow><annotation encoding=\"text\/plain\">cap V sub n plus 1 end-sub equals cap R cross cap V sub n<\/annotation><\/semantics><\/math><br><em>Where <\/em><math data-latex=\"R=1+\\frac{r}{100}\"><semantics><mrow><mi>R<\/mi><mo>=<\/mo><mn>1<\/mn><mo>+<\/mo><mfrac><mi>r<\/mi><mn>100<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">R=1+\\frac{r}{100}<\/annotation><\/semantics><\/math> <em>(interest per period)<\/em>.<\/li>\n\n\n\n<li><strong>Reducing Balance Loans &amp; Annuities (Combination):<\/strong> Includes both a multiplying factor (interest) and a constant addition\/subtraction (repayment or deposit).<br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>V<\/mi><mrow><mi>n<\/mi><mo>+<\/mo><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mi>R<\/mi><mo>\u00d7<\/mo><msub><mi>V<\/mi><mi>n<\/mi><\/msub><mo>\u00b1<\/mo><mi>D<\/mi><\/mrow><annotation encoding=\"text\/plain\">cap V sub n plus 1 end-sub equals cap R cross cap V sub n plus or minus cap D<\/annotation><\/semantics><\/math><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>2. Essential Components<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To fully define a recurrence relation in Unit 4, you must include:&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Initial Value (<\/strong><math data-latex=\"V_0\"><semantics><msub><mi>V<\/mi><mn>0<\/mn><\/msub><annotation encoding=\"application\/x-tex\">V_0<\/annotation><\/semantics><\/math><strong>):<\/strong> The starting principal or balance.<\/li>\n\n\n\n<li><strong>Rule (<\/strong><math data-latex=\"V_{n+1}\"><semantics><msub><mi>V<\/mi><mrow><mi>n<\/mi><mo>+<\/mo><mn>1<\/mn><\/mrow><\/msub><annotation encoding=\"application\/x-tex\">V_{n+1}<\/annotation><\/semantics><\/math><strong>):<\/strong> The formula connecting the current term (<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><msub><mi>V<\/mi><mi>n<\/mi><\/msub><annotation encoding=\"text\/plain\">cap V sub n<\/annotation><\/semantics><\/math>) to the next.<\/li>\n\n\n\n<li><strong>Time Period:<\/strong> Clear identification of the compounding or repayment frequency (e.g., monthly, fortnightly).&nbsp;<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">**********<strong>:<\/strong> <strong>reducing balance<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A reducing balance loan in QLD Year 12 General Mathematics (Unit 4: Financial Mathematics) is <mark>a loan where interest is calculated on the remaining balance rather than the original principal, with repayments made regularly<\/mark>. As repayments are made, the principal reduces, decreasing the interest charged over time.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Key Concepts of Reducing Balance (Loan\/Annuity):<\/strong>&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Definition:<\/strong> A compound interest application where interest charges decrease as the loan is paid off.<\/li>\n\n\n\n<li><strong>Recurrence Relation:<\/strong> Represented by the relation <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>V<\/mi><mrow><mi>n<\/mi><mo>+<\/mo><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mi>R<\/mi><msub><mi>V<\/mi><mi>n<\/mi><\/msub><mo>\u2212<\/mo><mi>M<\/mi><\/mrow><annotation encoding=\"text\/plain\">cap V sub n plus 1 end-sub equals cap R cap V sub n minus cap M<\/annotation><\/semantics><\/math>, where <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>R<\/mi><mo>=<\/mo><mn>1<\/mn><mo>+<\/mo><mfrac><mi>r<\/mi><mn>100<\/mn><\/mfrac><\/mrow><annotation encoding=\"text\/plain\">cap R equals 1 plus r over 100 end-fraction<\/annotation><\/semantics><\/math> (interest rate per period) and <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mi>M<\/mi><annotation encoding=\"text\/plain\">cap M<\/annotation><\/semantics><\/math> is the payment.<\/li>\n\n\n\n<li><strong>Formula:<\/strong> The balance <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mi>A<\/mi><annotation encoding=\"text\/plain\">cap A<\/annotation><\/semantics><\/math> after <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mi>n<\/mi><annotation encoding=\"text\/plain\">n<\/annotation><\/semantics><\/math> repayments is <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>A<\/mi><mo>=<\/mo><mi>P<\/mi><mo>(<\/mo><mn>1<\/mn><mo>+<\/mo><mi>i<\/mi><msup><mo>)<\/mo><mi>n<\/mi><\/msup><mo>\u2212<\/mo><mi>M<\/mi><mfrac><mrow><mo>(<\/mo><mn>1<\/mn><mo>+<\/mo><mi>i<\/mi><msup><mo>)<\/mo><mi>n<\/mi><\/msup><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><mi>i<\/mi><\/mfrac><\/mrow><annotation encoding=\"text\/plain\">cap A equals cap P open paren 1 plus i close paren to the n-th power minus cap M the fraction with numerator open paren 1 plus i close paren to the n-th power minus 1 and denominator i end-fraction<\/annotation><\/semantics><\/math>, where <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mi>P<\/mi><annotation encoding=\"text\/plain\">cap P<\/annotation><\/semantics><\/math> is principal, <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mi>i<\/mi><annotation encoding=\"text\/plain\">i<\/annotation><\/semantics><\/math> is interest rate per period, and <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mi>M<\/mi><annotation encoding=\"text\/plain\">cap M<\/annotation><\/semantics><\/math> is repayment.<\/li>\n\n\n\n<li><strong>Characteristics:<\/strong> The balance follows the pattern of a Present Value Annuity.<\/li>\n\n\n\n<li><strong>Final Payment:<\/strong> Often, the final repayment is adjusted to ensure the loan balance reaches exactly zero.&nbsp;<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Reducing balance loans are frequently used for mortgages and car loans.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">*******************  Supplements<strong>:<\/strong>  <strong>Annuities and Perpetuities<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Annuities and Perpetuities (QLD Year 12 General Maths, Unit 4) involve <mark>managing investments or loans with regular, equal payments over time<\/mark>. Annuities (e.g., retirement funds, loans) have a set end date, while Perpetuities are special investments where the principal remains constant, yielding interest-only payments forever.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Key Concepts in Unit 4 (Financial Math):<\/strong>&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Annuities:<\/strong> A series of equal, regular payments (e.g., superannuation or loan repayments). They are modeled using recurrence relations (<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>A<\/mi><mrow><mi>n<\/mi><mo>+<\/mo><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mi>r<\/mi><msub><mi>A<\/mi><mi>n<\/mi><\/msub><mo>\u00b1<\/mo><mi>d<\/mi><\/mrow><annotation encoding=\"text\/plain\">cap A sub n plus 1 end-sub equals r cap A sub n plus or minus d<\/annotation><\/semantics><\/math>) or financial solvers to find the future value (<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>F<\/mi><mi>V<\/mi><\/mrow><annotation encoding=\"text\/plain\">cap F cap V<\/annotation><\/semantics><\/math>) or present value (<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mi>V<\/mi><\/mrow><annotation encoding=\"text\/plain\">cap P cap V<\/annotation><\/semantics><\/math>).<\/li>\n\n\n\n<li><strong>Perpetuities:<\/strong> A type of annuity that continues indefinitely, paying out only the interest earned, meaning the principal balance remains constant (<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><msub><mi>V<\/mi><mn>0<\/mn><\/msub><annotation encoding=\"text\/plain\">cap V sub 0<\/annotation><\/semantics><\/math>).<\/li>\n\n\n\n<li><strong>Perpetuity Formula:<\/strong> <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo>=<\/mo><mfrac><mi>Q<\/mi><mi>i<\/mi><\/mfrac><\/mrow><annotation encoding=\"text\/plain\">cap P equals the fraction with numerator cap Q and denominator i end-fraction<\/annotation><\/semantics><\/math> (where <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mi>P<\/mi><annotation encoding=\"text\/plain\">cap P<\/annotation><\/semantics><\/math> is the principal, <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mi>Q<\/mi><annotation encoding=\"text\/plain\">cap Q<\/annotation><\/semantics><\/math> is the payment amount, and <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mi>i<\/mi><annotation encoding=\"text\/plain\">i<\/annotation><\/semantics><\/math> is the interest rate per period).<\/li>\n\n\n\n<li><strong>Calculation Methods:<\/strong>\n<ul class=\"wp-block-list\">\n<li><strong>Recurrence Relations:<\/strong> <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>A<\/mi><mrow><mi>n<\/mi><mo>+<\/mo><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mi>r<\/mi><msub><mi>A<\/mi><mi>n<\/mi><\/msub><mo>\u2212<\/mo><mi>d<\/mi><\/mrow><annotation encoding=\"text\/plain\">cap A sub n plus 1 end-sub equals r cap A sub n minus d<\/annotation><\/semantics><\/math> (for investments) or <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>A<\/mi><mrow><mi>n<\/mi><mo>+<\/mo><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mi>r<\/mi><msub><mi>A<\/mi><mi>n<\/mi><\/msub><mo>+<\/mo><mi>d<\/mi><\/mrow><annotation encoding=\"text\/plain\">cap A sub n plus 1 end-sub equals r cap A sub n plus d<\/annotation><\/semantics><\/math> (for loans).<\/li>\n\n\n\n<li><strong>Financial Calculators:<\/strong> TVM solvers (N, I%, PV, PMT, FV) are used for complex problems.&nbsp;<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Common Examples:<\/strong>&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Annuities:<\/strong> Saving for retirement by contributing <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo>$<\/mo><mn>500<\/mn><\/mrow><annotation encoding=\"text\/plain\">$ 500<\/annotation><\/semantics><\/math> monthly, or repaying a car loan.<\/li>\n\n\n\n<li><strong>Perpetuities:<\/strong> A charitable fund that generates <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo>$<\/mo><mn>10<\/mn><mo>,<\/mo><mn>000<\/mn><\/mrow><annotation encoding=\"text\/plain\">$ 10 comma 000<\/annotation><\/semantics><\/math> interest every year to pay for a scholarship, leaving the original <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo>$<\/mo><mn>200<\/mn><mo>,<\/mo><mn>000<\/mn><\/mrow><annotation encoding=\"text\/plain\">$ 200 comma 000<\/annotation><\/semantics><\/math> donation untouched.\u00a0<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">********************************************************************************************************************************************************<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">QLD 12\u5e74\u751f\u4e00\u822c\u6570\u5b66\uff08\u6295\u8cc7\u3068\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\uff09\u306e\u30e6\u30cb\u30c3\u30c84\u306f\u3001\u5b9f\u7528\u7684\u306a\u91d1\u878d\u5fdc\u7528\u3068\u30b0\u30e9\u30d5\u7406\u8ad6\u306b\u7126\u70b9\u3092\u5f53\u3066\u3066\u3044\u307e\u3059\u3002\u8907\u5229\u3001\u30ed\u30fc\u30f3\u3001\u5e74\u91d1\u3001\u6c38\u4e45\u50b5\u306e\u8a08\u7b97\uff08\u30c8\u30d4\u30c3\u30af1\uff09\u306b\u52a0\u3048\u3001\u30b0\u30e9\u30d5\u3001\u30d1\u30b9\u3001\u30c8\u30ec\u30a4\u30eb\u3001\u30aa\u30a4\u30e9\u30fc\u30b0\u30e9\u30d5\uff0f\u30cf\u30df\u30eb\u30c8\u30f3\u30b0\u30e9\u30d5\u3068\u3044\u3063\u305f\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u6982\u5ff5\u3092\u6271\u3044\u3001\u610f\u601d\u6c7a\u5b9a\u3092\u30e2\u30c7\u30eb\u5316\u3057\u307e\u3059\uff08\u30c8\u30d4\u30c3\u30af1\uff09\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u30e6\u30cb\u30c3\u30c84\u306e\u4e3b\u8981\u30c8\u30d4\u30c3\u30af\uff1a\u4e00\u822c\u6570\u5b66<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u30c8\u30d4\u30c3\u30af1\uff1a\u30ed\u30fc\u30f3\u3001\u6295\u8cc7\u3001\u5e74\u91d1<br>\u8907\u5229\uff1a\u8a08\u7b97\u3001\u6f38\u5316\u5f0f\u306e\u5229\u7528\u3001\u8907\u5229\u5f0f\u306e\u9069\u7528\u3002<br>\u91d1\u878d\u5fdc\u7528\uff1a\u9013\u6e1b\u578b\u30ed\u30fc\u30f3\u3001\u5e74\u91d1\u3001\u6c38\u4e45\u50b5\u3002\u5229\u7387\uff1a\u5b9f\u52b9\u5e74\u5229\u7387\u306e\u7406\u89e3\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u306e\u5358\u5143\u3067\u306f\u3001\u5b66\u751f\u304c\u73fe\u5b9f\u4e16\u754c\u306e\u91d1\u878d\u7ba1\u7406\u3068\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u3092\u7528\u3044\u305f\u6700\u9069\u5316\u554f\u984c\u306e\u89e3\u6c7a\u306b\u5099\u3048\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">*********************************<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u30af\u30a4\u30fc\u30f3\u30ba\u30e9\u30f3\u30c9\u5dde\uff08QLD\uff09\u306e12\u5e74\u751f\u4e00\u822c\u6570\u5b66\u30b7\u30e9\u30d0\u30b9\u3067\u306f\u3001\u300c\u30b0\u30e9\u30d5\u3068\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u300d\uff08\u4e3b\u306b\u30e6\u30cb\u30c3\u30c84\uff09\u3068\u300c\u30ed\u30fc\u30f3\u3001\u6295\u8cc7\u3001\u5e74\u91d1\u300d\uff08\u6295\u8cc7\u3084\u91d1\u878d\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u3068\u4e26\u3093\u3067\u3088\u304f\u8a00\u53ca\u3055\u308c\u308b\uff09\u304c\u30ab\u30ea\u30ad\u30e5\u30e9\u30e0\u306e\u4e3b\u8981\u69cb\u6210\u8981\u7d20\u3068\u306a\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u300c\u30b0\u30e9\u30d5\u3068\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u300d\u3068\u300c\u6295\u8cc7\u300d\u306e\u5074\u9762\u306b\u7126\u70b9\u3092\u5f53\u3066\u3001\u4e3b\u8981\u30c8\u30d4\u30c3\u30af\u3092\u5206\u985e\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u30ed\u30fc\u30f3\u3001\u6295\u8cc7\u3001\u5e74\u91d1\uff08\u30e6\u30cb\u30c3\u30c84\uff1a\u91d1\u878d\u6570\u5b66\uff09<br>\u3053\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u300c\u6295\u8cc7\u3068\u91d1\u878d\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u300d\u306e\u5074\u9762\u3092\u6271\u3044\u3001\u30b7\u30fc\u30b1\u30f3\u30b9\u3068\u518d\u5e30\u3092\u7528\u3044\u3066\u91d1\u878d\u72b6\u6cc1\u3092\u30e2\u30c7\u30eb\u5316\u3059\u308b\u3053\u3068\u306b\u7126\u70b9\u3092\u5f53\u3066\u308b\u3002<\/li>\n<\/ol>\n\n\n\n<ol start=\"2\" class=\"wp-block-list\">\n<li><\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u8907\u5229<\/strong>\uff1a\u518d\u5e30\u95a2\u4fc2\u3092\u7528\u3044\u3066\u8907\u5229\u6295\u8cc7\u306e\u554f\u984c\u3092\u30e2\u30c7\u30eb\u5316\u3057\u3001\u89e3\u304f\u3002<br><strong>\u5b9f\u52b9\u5e74\u5229\u7387<\/strong>\uff1a\u5e74\u9593\u306e\u5b9f\u8cea\u91d1\u5229\u3092\u8a08\u7b97\u3059\u308b\u3002<br><strong>\u9013\u6e1b\u6b8b\u9ad8\u30ed\u30fc\u30f3<\/strong>\uff1a\u518d\u5e30\u6cd5\u3092\u7528\u3044\u3066\u3001\u9013\u6e1b\u6b8b\u9ad8\u306b\u57fa\u3065\u3044\u3066\u5229\u606f\u3092\u8a08\u7b97\u3059\u308b\u30ed\u30fc\u30f3\u3092\u30e2\u30c7\u30eb\u5316\u3057\u3001\u652f\u6255\u984d\u3092\u6c7a\u5b9a\u3059\u308b\u3002<br><strong>\u5e74\u91d1\u3068\u6c38\u4e45\u5e74\u91d1<\/strong>\uff1a\u5e74\u91d1\uff08\u5b9a\u671f\u7684\u306a\u53ce\u5165\u304c\u652f\u6255\u308f\u308c\u308b\u6295\u8cc7\uff09\u3068\u6c38\u4e45\u5e74\u91d1\u306b\u3064\u3044\u3066\u7406\u89e3\u3059\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">*************************<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">** \u88dc\u8db3\uff1a\u6f38\u5316\u5f0f<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">QLD 12\u5e74\u751f \u4e00\u822c\u6570\u5b66\uff08\u30e6\u30cb\u30c3\u30c84\uff09\u306b\u304a\u3044\u3066\u3001\u6f38\u5316\u5f0f\u3068\u306f\u3001\u5404\u9805\u3092\u524d\u306e\u9805\u306e\u5024\u306b\u57fa\u3065\u3044\u3066\u5b9a\u7fa9\u3059\u308b\u3053\u3068\u3067\u91d1\u878d\u72b6\u6cc1\u3092\u30e2\u30c7\u30eb\u5316\u3059\u308b\u305f\u3081\u306b\u7528\u3044\u3089\u308c\u308b\u6570\u5b66\u7684\u898f\u5247\u3067\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u4e3b\u8981\u306a\u91d1\u878d\u30e2\u30c7\u30eb<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u91d1\u878d\u5fdc\u7528\u306f\u3001\u4e3b\u306b3\u7a2e\u985e\u306e\u6f38\u5316\u5f0f\u306b\u5206\u985e\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5358\u5229\uff08\u7dda\u5f62\u5897\u52a0\uff0f\u6e1b\u5c11\uff09\uff1a\u5b9a\u6570\u3092\u52a0\u7b97\u307e\u305f\u306f\u6e1b\u7b97\u3057\u307e\u3059\u3002<br><math data-latex=\"V_{n+1}=V_n+D\"><semantics><mrow><msub><mi>V<\/mi><mrow><mi>n<\/mi><mo>+<\/mo><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><msub><mi>V<\/mi><mi>n<\/mi><\/msub><mo>+<\/mo><mi>D<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">V_{n+1}=V_n+D<\/annotation><\/semantics><\/math><br>\u305f\u3060\u3057\u3001<math data-latex=\"D=\\frac{r}{100}\u00d7V_0\"><semantics><mrow><mi>D<\/mi><mo>=<\/mo><mfrac><mi>r<\/mi><mn>100<\/mn><\/mfrac><mo>\u00d7<\/mo><msub><mi>V<\/mi><mn>0<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">D=\\frac{r}{100}\u00d7V_0<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8907\u5229\uff08\u7b49\u6bd4\u7d1a\u6570\u5897\u52a0\uff0f\u6e1b\u5c11\uff09\uff1a\u5024\u306b\u5b9a\u6570\u3092\u4e57\u3058\u307e\u3059\u3002<br><math data-latex=\"V_{n+1}=R\u00d7V_n\"><semantics><mrow><msub><mi>V<\/mi><mrow><mi>n<\/mi><mo>+<\/mo><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mi>R<\/mi><mo>\u00d7<\/mo><msub><mi>V<\/mi><mi>n<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">V_{n+1}=R\u00d7V_n<\/annotation><\/semantics><\/math><br>\u305f\u3060\u3057\u3001<math data-latex=\"R=1+\\frac{r}{100}\"><semantics><mrow><mi>R<\/mi><mo>=<\/mo><mn>1<\/mn><mo>+<\/mo><mfrac><mi>r<\/mi><mn>100<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">R=1+\\frac{r}{100}<\/annotation><\/semantics><\/math>\uff081\u671f\u9593\u3042\u305f\u308a\u306e\u5229\u606f\uff09<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u9013\u6e1b\u578b\u30ed\u30fc\u30f3\u304a\u3088\u3073\u5e74\u91d1\uff08\u7d44\u307f\u5408\u308f\u305b\uff09\uff1a\u4e57\u6570\uff08\u5229\u606f\uff09\u3068\u5b9a\u6570\u306e\u52a0\u7b97\uff0f\u6e1b\u7b97\uff08\u8fd4\u6e08\u307e\u305f\u306f\u9810\u91d1\uff09\u306e\u4e21\u65b9\u304c\u542b\u307e\u308c\u307e\u3059\u3002<br><math data-latex=\"V_{n+1}=R\u00d7V_n\u00b1D\"><semantics><mrow><msub><mi>V<\/mi><mrow><mi>n<\/mi><mo>+<\/mo><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mi>R<\/mi><mo>\u00d7<\/mo><msub><mi>V<\/mi><mi>n<\/mi><\/msub><mo>\u00b1<\/mo><mi>D<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">V_{n+1}=R\u00d7V_n\u00b1D<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<ol start=\"2\" class=\"wp-block-list\">\n<li>\u5fc5\u9808\u69cb\u6210\u8981\u7d20<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u30e6\u30cb\u30c3\u30c84\u3067\u6f38\u5316\u5f0f\u3092\u5b8c\u5168\u306b\u5b9a\u7fa9\u3059\u308b\u306b\u306f\u3001\u4ee5\u4e0b\u306e\u8981\u7d20\u3092\u542b\u3081\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u521d\u671f\u5024\uff08<math data-latex=\"V0\"><semantics><mrow><mi>V<\/mi><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">V0<\/annotation><\/semantics><\/math>\uff09\uff1a\u958b\u59cb\u6642\u306e\u5143\u672c\u307e\u305f\u306f\u6b8b\u9ad8\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u898f\u5247\uff08<math data-latex=\"V_{n+1}\"><semantics><msub><mi>V<\/mi><mrow><mi>n<\/mi><mo>+<\/mo><mn>1<\/mn><\/mrow><\/msub><annotation encoding=\"application\/x-tex\">V_{n+1}<\/annotation><\/semantics><\/math>\uff09\uff1a\u73fe\u5728\u306e\u671f\u9593\uff08<math data-latex=\"V_n\"><semantics><msub><mi>V<\/mi><mi>n<\/mi><\/msub><annotation encoding=\"application\/x-tex\">V_n<\/annotation><\/semantics><\/math>\uff09\u3068\u6b21\u306e\u671f\u9593\u3092\u7d50\u3073\u3064\u3051\u308b\u5f0f\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u671f\u9593\uff1a\u8907\u5229\u8a08\u7b97\u307e\u305f\u306f\u8fd4\u6e08\u983b\u5ea6\uff08\u4f8b\uff1a\u6bce\u6708\u3001\u9694\u9031\uff09\u3092\u660e\u78ba\u306b\u793a\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">** \u88dc\u8db3\u8cc7\u6599\uff1a\u9013\u6e1b\u6b8b\u9ad8<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">QLD 12\u5e74\u751f\u4e00\u822c\u6570\u5b66\uff08\u30e6\u30cb\u30c3\u30c84\uff1a\u91d1\u878d\u6570\u5b66\uff09\u306b\u304a\u3051\u308b\u9013\u6e1b\u6b8b\u9ad8\u30ed\u30fc\u30f3\u3068\u306f\u3001\u5229\u606f\u304c\u5143\u306e\u5143\u672c\u3067\u306f\u306a\u304f\u6b8b\u9ad8\u306b\u57fa\u3065\u3044\u3066\u8a08\u7b97\u3055\u308c\u3001\u5b9a\u671f\u7684\u306b\u8fd4\u6e08\u3055\u308c\u308b\u30ed\u30fc\u30f3\u3067\u3059\u3002\u8fd4\u6e08\u304c\u9032\u3080\u306b\u3064\u308c\u3066\u5143\u672c\u304c\u6e1b\u5c11\u3057\u3001\u6642\u9593\u306e\u7d4c\u904e\u3068\u3068\u3082\u306b\u5229\u606f\u304c\u6e1b\u5c11\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u9013\u6e1b\u6b8b\u9ad8\uff08\u30ed\u30fc\u30f3\uff0f\u5e74\u91d1\uff09\u306e\u4e3b\u8981\u6982\u5ff5\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5b9a\u7fa9\uff1a\u30ed\u30fc\u30f3\u306e\u8fd4\u6e08\u304c\u9032\u3080\u306b\u3064\u308c\u3066\u5229\u606f\u304c\u6e1b\u5c11\u3059\u308b\u8907\u5229\u306e\u9069\u7528\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u518d\u5e30\u95a2\u4fc2\uff1a<math data-latex=\" V_{n+1}=RV_{n}-M\"><semantics><mrow><msub><mi>V<\/mi><mrow><mi>n<\/mi><mo>+<\/mo><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mi>R<\/mi><msub><mi>V<\/mi><mi>n<\/mi><\/msub><mo>\u2212<\/mo><mi>M<\/mi><\/mrow><annotation encoding=\"application\/x-tex\"> V_{n+1}=RV_{n}-M<\/annotation><\/semantics><\/math> \u306e\u95a2\u4fc2\u5f0f\u3067\u8868\u3055\u308c\u307e\u3059\u3002\u3053\u3053\u3067\u3001<math data-latex=\"R=1+\\frac{r}{100}\"><semantics><mrow><mi>R<\/mi><mo>=<\/mo><mn>1<\/mn><mo>+<\/mo><mfrac><mi>r<\/mi><mn>100<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">R=1+\\frac{r}{100}<\/annotation><\/semantics><\/math>\uff08\u671f\u9593\u3042\u305f\u308a\u306e\u5229\u7387\uff09\u3001<math data-latex=\"M \"><semantics><mi>M<\/mi><annotation encoding=\"application\/x-tex\">M <\/annotation><\/semantics><\/math>\u306f\u8fd4\u6e08\u984d\u3067\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u516c\u5f0f\uff1an\u56de\u306e\u8fd4\u6e08\u5f8c\u306e\u6b8b\u9ad8 A \u306f A=P(1+i)n\u2212M(1+i)n\u22121 \u3067\u3059\u3002\u3053\u3053\u3067\u3001P \u306f\u5143\u672c\u3001i \u306f\u671f\u9593\u3042\u305f\u308a\u306e\u5229\u7387\u3001M \u306f\u8fd4\u6e08\u984d\u3067\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7279\u5fb4\uff1a\u6b8b\u9ad8\u306f\u73fe\u5728\u4fa1\u5024\u5e74\u91d1\u306e\u30d1\u30bf\u30fc\u30f3\u306b\u5f93\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6700\u7d42\u8fd4\u6e08\u984d\uff1a\u591a\u304f\u306e\u5834\u5408\u3001\u6700\u7d42\u8fd4\u6e08\u984d\u306f\u30ed\u30fc\u30f3\u6b8b\u9ad8\u304c\u3061\u3087\u3046\u3069\u30bc\u30ed\u306b\u306a\u308b\u3088\u3046\u306b\u8abf\u6574\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6e1b\u984d\u578b\u30ed\u30fc\u30f3\u306f\u3001\u4f4f\u5b85\u30ed\u30fc\u30f3\u3084\u81ea\u52d5\u8eca\u30ed\u30fc\u30f3\u3067\u3088\u304f\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>*<\/strong> \u88dc\u8db3\u8cc7\u6599\uff1a\u5e74\u91d1\u3068\u6c38\u4e45\u50b5<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5e74\u91d1\u3068\u6c38\u4e45\u50b5\uff08QLD 12\u5e74\u751f \u4e00\u822c\u6570\u5b66\u3001\u30e6\u30cb\u30c3\u30c84\uff09\u306f\u3001\u4e00\u5b9a\u671f\u9593\u306b\u308f\u305f\u3063\u3066\u5b9a\u671f\u7684\u306b\u5747\u7b49\u8fd4\u6e08\u3092\u884c\u3046\u6295\u8cc7\u307e\u305f\u306f\u30ed\u30fc\u30f3\u306e\u7ba1\u7406\u306b\u95a2\u3059\u308b\u3082\u306e\u3067\u3059\u3002\u5e74\u91d1\uff08\u4f8b\uff1a\u9000\u8077\u91d1\u3001\u30ed\u30fc\u30f3\uff09\u306b\u306f\u7d42\u4e86\u65e5\u304c\u8a2d\u5b9a\u3055\u308c\u3066\u3044\u307e\u3059\u304c\u3001\u6c38\u4e45\u5e74\u91d1\u306f\u5143\u672c\u304c\u4e00\u5b9a\u3067\u3001\u5229\u606f\u306e\u307f\u304c\u6c38\u4e45\u306b\u652f\u6255\u308f\u308c\u308b\u7279\u5225\u306a\u6295\u8cc7\u3067\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u30e6\u30cb\u30c3\u30c84\uff08\u91d1\u878d\u6570\u5b66\uff09\u306e\u4e3b\u8981\u6982\u5ff5\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5e74\u91d1\uff1a\u5b9a\u671f\u7684\u306b\u540c\u984d\u306e\u652f\u6255\u3044\u304c\u884c\u308f\u308c\u308b\u3082\u306e\uff08\u4f8b\uff1a\u5e74\u91d1\u3084\u30ed\u30fc\u30f3\u306e\u8fd4\u6e08\uff09\u3002\u3053\u308c\u3089\u306f\u3001\u5c06\u6765\u4fa1\u5024\uff08<math data-latex=\"FV\"><semantics><mrow><mi>F<\/mi><mi>V<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">FV<\/annotation><\/semantics><\/math>\uff09\u307e\u305f\u306f\u73fe\u5728\u4fa1\u5024\uff08<math data-latex=\"PV\"><semantics><mrow><mi>P<\/mi><mi>V<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">PV<\/annotation><\/semantics><\/math>\uff09\u3092\u6c42\u3081\u308b\u305f\u3081\u306b\u3001\u56de\u5e30\u95a2\u4fc2\uff08<math data-latex=\"A_{n+1}=rA_n\u00b1d\"><semantics><mrow><msub><mi>A<\/mi><mrow><mi>n<\/mi><mo>+<\/mo><mn>1<\/mn><\/mrow><\/msub><mo>=<\/mo><mi>r<\/mi><msub><mi>A<\/mi><mi>n<\/mi><\/msub><mo>\u00b1<\/mo><mi>d<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">A_{n+1}=rA_n\u00b1d<\/annotation><\/semantics><\/math>\uff09\u307e\u305f\u306f\u91d1\u878d\u30bd\u30eb\u30d0\u30fc\u3092\u7528\u3044\u3066\u30e2\u30c7\u30eb\u5316\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6c38\u4e45\u5e74\u91d1\uff1a\u7121\u671f\u9650\u306b\u7d99\u7d9a\u3059\u308b\u5e74\u91d1\u306e\u4e00\u7a2e\u3067\u3001\u5229\u606f\u306e\u307f\u304c\u652f\u6255\u308f\u308c\u308b\u305f\u3081\u3001\u5143\u672c\u6b8b\u9ad8\uff08<math data-latex=\"V0\"><semantics><mrow><mi>V<\/mi><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">V0<\/annotation><\/semantics><\/math>\uff09\u306f\u4e00\u5b9a\u3067\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6c38\u4e45\u5e74\u91d1\u306e\u516c\u5f0f\uff1a<math data-latex=\"P = \\frac{Q}{i}\"><semantics><mrow><mi>P<\/mi><mo>=<\/mo><mfrac><mi>Q<\/mi><mi>i<\/mi><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P = \\frac{Q}{i}<\/annotation><\/semantics><\/math>\uff08 P\u306f\u5143\u672c\u3001Q\u306f\u652f\u6255\u984d\u3001i\u306f\u671f\u9593\u3054\u3068\u306e\u5229\u7387\uff09\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8a08\u7b97\u65b9\u6cd5\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u56de\u5e30\u95a2\u4fc2\uff1a<math data-latex=\"An+1=rAn\u2212d\"><semantics><mrow><mi>A<\/mi><mi>n<\/mi><mo>+<\/mo><mn>1<\/mn><mo>=<\/mo><mi>r<\/mi><mi>A<\/mi><mi>n<\/mi><mo>\u2212<\/mo><mi>d<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">An+1=rAn\u2212d<\/annotation><\/semantics><\/math>\uff08\u6295\u8cc7\u306e\u5834\u5408\uff09\u307e\u305f\u306f<math data-latex=\"An+1=rAn+d\"><semantics><mrow><mi>A<\/mi><mi>n<\/mi><mo>+<\/mo><mn>1<\/mn><mo>=<\/mo><mi>r<\/mi><mi>A<\/mi><mi>n<\/mi><mo>+<\/mo><mi>d<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">An+1=rAn+d<\/annotation><\/semantics><\/math>\uff08\u30ed\u30fc\u30f3\u306e\u5834\u5408\uff09\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8ca1\u52d9\u8a08\u7b97\u30c4\u30fc\u30eb\uff1aTVM\u30bd\u30eb\u30d0\u30fc\uff08N\u3001I%\u3001PV\u3001PMT\u3001FV\uff09\u306f\u8907\u96d1\u306a\u554f\u984c\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e00\u822c\u7684\u306a\u4f8b\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5e74\u91d1\uff1a\u6bce\u6708500\u30c9\u30eb\u3092\u62e0\u51fa\u3057\u3066\u9000\u8077\u5f8c\u306e\u8caf\u84c4\u3092\u3057\u305f\u308a\u3001\u81ea\u52d5\u8eca\u30ed\u30fc\u30f3\u3092\u8fd4\u6e08\u3057\u305f\u308a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6c38\u4e45\u57fa\u91d1\uff1a\u6bce\u5e741\u4e07\u30c9\u30eb\u306e\u5229\u606f\u3092\u751f\u307f\u51fa\u3057\u3001\u5968\u5b66\u91d1\u306e\u8fd4\u6e08\u306b\u5145\u3066\u3001\u5143\u306e\u5bc4\u4ed8\u91d120\u4e07\u30c9\u30eb\u306f\u305d\u306e\u307e\u307e\u6b8b\u3059\u6148\u5584\u57fa\u91d1\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Unit 4 of QLD Year 12 General Mathematics (Investing and Networking) focuses on practical financial applications and graph theory. It covers compound interest, loans, annuities, and perpetuity calculations (Topic 1) , alongside network concepts such as graphs, paths, trails, and,Eulerian\/Hamiltonian graphs for modeling decision-making (Topic 2).&nbsp; Key Topics in Unit 4: General Mathematics&nbsp; This unit [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8],"tags":[],"class_list":["post-1292","post","type-post","status-publish","format-standard","hentry","category-math"],"_links":{"self":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts\/1292","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1292"}],"version-history":[{"count":8,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts\/1292\/revisions"}],"predecessor-version":[{"id":1366,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts\/1292\/revisions\/1366"}],"wp:attachment":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1292"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1292"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1292"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}