{"id":964,"date":"2026-01-04T14:36:14","date_gmt":"2026-01-04T04:36:14","guid":{"rendered":"https:\/\/archive4ones.com\/2ndstudy\/?p=964"},"modified":"2026-01-04T14:36:14","modified_gmt":"2026-01-04T04:36:14","slug":"year11-math-2-2-1-warm-up-questions-consumer-arithmetic-general-mathematics","status":"publish","type":"post","link":"https:\/\/archive4ones.com\/2ndstudy\/?p=964","title":{"rendered":"Year11 MATH 2-2-1 Warm-up Questions-Consumer Arithmetic (General Mathematics)"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To prepare you for the rigors of <strong>Unit 1 General Mathematics<\/strong>, these warm-up questions focus on the financial modeling skills required for high-achieving students. We will move beyond simple calculations to explore the &#8220;Time Value of Money,&#8221; the impact of compounding periods, and the nuances of inflation.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Warm-up: Consumer Arithmetic (General Mathematics)<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Q-1.  An investor places $10,000 into a savings account that earns 4.5% per annum simple interest. How much interest will they have earned at the end of 6 years?<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">A. $3,022.60<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. $450<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. $12,700<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. $2,700<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hint:  The formula for simple interest is&nbsp;<strong><em>I<\/em>=<em>Prt<\/em><\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Q-2. A $5,000 investment earns 6% per annum interest compounded monthly. Which of the following correctly identifies the values for the periodic interest rate (r) and the number of periods (n) after 3 years?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A. <em>r<\/em>=0.005, <em>n<\/em>=3<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. <em>r<\/em>=0.06, <em>n<\/em>=36<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. <em>r<\/em>=0.06, <em>n<\/em>=3<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. <em>r<\/em>=0.005, <em>n<\/em>=36<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hint:  Divide the annual rate by the number of compounds per year and multiply the years by the same number.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Q-3. If a pair of shoes costs $120 today and the average annual inflation rate is 3%, what is the predicted cost of the same shoes in 5 years, rounded to the nearest cent?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A. $139.11<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. $123.60<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. $156.00<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. $138.00<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hint:  Think of inflation as a price that compounds annually like a bank account.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Q-4. The total price of a laptop, including <math data-latex=\"10\\%\"><semantics><mrow><mn>10<\/mn><mi>%<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">10\\%<\/annotation><\/semantics><\/math> GST, is <math data-latex=\"\\$1,650\"><semantics><mrow><mi>$<\/mi><mn>1,650<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\$1,650<\/annotation><\/semantics><\/math>. What was the price of the laptop before GST was added?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A. $1,485<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. $1,500<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. $1,815<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. $1,600<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hint:  Remember that the final price is&nbsp;110%&nbsp;of the original price.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Q-5. A stock price increases by <math data-latex=\"20\\%\"><semantics><mrow><mn>20<\/mn><mi>%<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">20\\%<\/annotation><\/semantics><\/math> in its first year but decreases by <math data-latex=\"20\\%\"><semantics><mrow><mn>20<\/mn><mi>%<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">20\\%<\/annotation><\/semantics><\/math> in its second year. How does the final price compare to the original price?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A. It is 2% lower than the original price.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. It is 4% higher than the original price.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. It is exactly the same as the original price.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. It is 4% lower than the original price.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hint:  Try calculating the result starting with&nbsp;$100&nbsp;as your base value.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Q-6. Which investment option provides the best return: a nominal rate of <math data-latex=\"12\\%\"><semantics><mrow><mn>12<\/mn><mi>%<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">12\\%<\/annotation><\/semantics><\/math> p.a. compounded annually, or a nominal rate of <math data-latex=\"11.8\\%\"><semantics><mrow><mn>11.8<\/mn><mi>%<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">11.8\\%<\/annotation><\/semantics><\/math> p.a. compounded monthly?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A. Neither, as both result in a loss after inflation.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. The 12% compounded annually is better.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. They are exactly the same.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. The 11.8% compounded monthly is better.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hint:  Calculate the effective annual rate for the monthly compounding option to compare &#8216;apples to apples&#8217;.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Q-7. An antique car is valued at <math data-latex=\"\\$50,000\"><semantics><mrow><mi>$<\/mi><mn>50,000<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\$50,000<\/annotation><\/semantics><\/math> and is expected to appreciate at a rate of <math data-latex=\"8\\%\"><semantics><mrow><mn>8<\/mn><mi>%<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">8\\%<\/annotation><\/semantics><\/math> per year. Which formula models its value (<math data-latex=\"V\"><semantics><mi>V<\/mi><annotation encoding=\"application\/x-tex\">V<\/annotation><\/semantics><\/math>) after <math data-latex=\"t\"><semantics><mi>t<\/mi><annotation encoding=\"application\/x-tex\">t<\/annotation><\/semantics><\/math> years?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A. <em>V<\/em>=50,000(0.08)<em>t<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. <em>V<\/em>=50,000(1.08)<em>t<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. <em>V<\/em>=50,000(0.92)<em>t<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. <em>V<\/em>=50,000+(0.08\u00d7<em>t<\/em>)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hint:  Appreciation means the value is growing over time.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Q-8. A &#8216;Reducing Balance&#8217; depreciation model for a piece of machinery worth <math data-latex=\"\\$20,000\"><semantics><mrow><mi>$<\/mi><mn>20,000<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\$20,000<\/annotation><\/semantics><\/math> uses a rate of <math data-latex=\"15\\%\"><semantics><mrow><mn>15<\/mn><mi>%<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">15\\%<\/annotation><\/semantics><\/math> p.a. What is its book value after <math data-latex=\"2\"><semantics><mn>2<\/mn><annotation encoding=\"application\/x-tex\">2<\/annotation><\/semantics><\/math> years?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A. $14,450<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. $26,450<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. $14,000<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. $17,000<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hint:  Reducing balance means the value is multiplied by&nbsp;(1\u2212<em>r<\/em>)&nbsp;each year.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Q-9. If your bank account earns 5% interest but inflation is 3%, what is the &#8216;real&#8217; rate of return on your investment?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A. 8%<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. 1.67%<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. 2%<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. 5%<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hint:  Subtract the loss of purchasing power from the gain in interest.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><br>Q-10.  A student needs $10,000 in 4 years. If they can get a savings rate of 5% p.a. compounded annually, how much do they need to invest today? (Round to the nearest dollar)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A. $8,227<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. $8,000<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. $12,155<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. $7,835<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hint:  You are looking for the &#8216;Principal&#8217; (<em>P<\/em>) in the compound interest formula    &nbsp;<em>A<\/em>=<em>P<\/em>(1+<em>r<\/em>)<em>n<\/em>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">==================<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Great job completing the warm-up! These questions touched on some of the core themes of <strong>General Mathematics<\/strong>\u2014specifically, how time and frequency of compounding can drastically change financial outcomes. Keep practicing these rearrangements of the interest formulas!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">********************************************************************************************************************************************************<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u30e6\u30cb\u30c3\u30c81\u300c\u4e00\u822c\u6570\u5b66\u300d\u306e\u96e3\u95a2\u306b\u5099\u3048\u308b\u305f\u3081\u306b\u3001\u3053\u308c\u3089\u306e\u30a6\u30a9\u30fc\u30e0\u30a2\u30c3\u30d7\u554f\u984c\u306f\u3001\u512a\u79c0\u306a\u751f\u5f92\u306b\u6c42\u3081\u3089\u308c\u308b\u8ca1\u52d9\u30e2\u30c7\u30ea\u30f3\u30b0\u30b9\u30ad\u30eb\u306b\u7126\u70b9\u3092\u5f53\u3066\u3066\u3044\u307e\u3059\u3002\u5358\u7d14\u306a\u8a08\u7b97\u306b\u3068\u3069\u307e\u3089\u305a\u3001\u300c\u8ca8\u5e63\u306e\u6642\u9593\u4fa1\u5024\u300d\u3001\u8907\u5229\u671f\u9593\u306e\u5f71\u97ff\u3001\u305d\u3057\u3066\u30a4\u30f3\u30d5\u30ec\u306e\u30cb\u30e5\u30a2\u30f3\u30b9\u307e\u3067\u6398\u308a\u4e0b\u3052\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u554f-1. \u3042\u308b\u6295\u8cc7\u5bb6\u304c\u3001\u5e74\u52294.5%\u306e\u5358\u5229\u4ed8\u304d\u666e\u901a\u9810\u91d1\u53e3\u5ea7\u306b10,000\u30c9\u30eb\u3092\u9810\u3051\u5165\u308c\u307e\u3057\u305f\u30026\u5e74\u5f8c\u306b\u306f\u3044\u304f\u3089\u306e\u5229\u606f\u304c\u5f97\u3089\u308c\u308b\u3067\u3057\u3087\u3046\u304b\uff1f<br>\u30d2\u30f3\u30c8\uff1a\u5358\u5229\u306e\u516c\u5f0f\u306fI=Prt\u3067\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u554f-2. 5,000\u30c9\u30eb\u3092\u6295\u8cc7\u3059\u308b\u3068\u3001\u6708\u52296%\u306e\u8907\u5229\u304c\u5f97\u3089\u308c\u307e\u3059\u30023\u5e74\u5f8c\u306e\u671f\u9593\u5229\u7387\uff08r\uff09\u3068\u671f\u9593\u6570\uff08n\uff09\u306e\u5024\u3092\u6b63\u3057\u304f\u793a\u3057\u3066\u3044\u308b\u306e\u306f\u6b21\u306e\u3046\u3061\u3069\u308c\u3067\u3059\u304b\uff1f<br>\u30d2\u30f3\u30c8\uff1a\u5e74\u5229\u7387\u3092\u5e74\u9593\u8907\u5229\u56de\u6570\u3067\u5272\u308a\u3001\u540c\u3058\u56de\u6570\u3092\u5e74\u6570\u306b\u639b\u3051\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u554f-3. \u97741\u8db3\u306e\u73fe\u5728\u306e\u4fa1\u683c\u304c120\u30c9\u30eb\u3067\u3001\u5e74\u9593\u5e73\u5747\u30a4\u30f3\u30d5\u30ec\u7387\u304c3%\u306e\u5834\u5408\u3001\u540c\u3058\u9774\u306e5\u5e74\u5f8c\u306e\u4e88\u6e2c\u4fa1\u683c\u306f\u3044\u304f\u3089\u306b\u306a\u308b\u3067\u3057\u3087\u3046\u304b\uff1f\uff08\u7aef\u6570\u306f\u5207\u308a\u6368\u3066\uff09<br>\u30d2\u30f3\u30c8\uff1a\u30a4\u30f3\u30d5\u30ec\u306f\u3001\u9280\u884c\u53e3\u5ea7\u306e\u3088\u3046\u306b\u6bce\u5e74\u8907\u5229\u3067\u8a08\u7b97\u3055\u308c\u308b\u4fa1\u683c\u3068\u8003\u3048\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u554f-4. \u30ce\u30fc\u30c8\u30d1\u30bd\u30b3\u30f3\u306e\u5408\u8a08\u4fa1\u683c\u306f\u3001GST 10% \u3092\u542b\u3081\u3066 1,650 \u30c9\u30eb\u3067\u3059\u3002GST \u304c\u52a0\u7b97\u3055\u308c\u308b\u524d\u306e\u30ce\u30fc\u30c8\u30d1\u30bd\u30b3\u30f3\u306e\u4fa1\u683c\u306f\u3044\u304f\u3089\u3067\u3057\u305f\u304b\uff1f<br>\u30d2\u30f3\u30c8\uff1a\u6700\u7d42\u4fa1\u683c\u306f\u5f53\u521d\u4fa1\u683c\u306e 110% \u3067\u3042\u308b\u3053\u3068\u3092\u899a\u3048\u3066\u304a\u3044\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u554f-5. \u3042\u308b\u682a\u4fa1\u304c 1 \u5e74\u76ee\u306b 20% \u4e0a\u6607\u3057\u307e\u3057\u305f\u304c\u30012 \u5e74\u76ee\u306b 20% \u4e0b\u843d\u3057\u307e\u3057\u305f\u3002\u6700\u7d42\u4fa1\u683c\u306f\u5f53\u521d\u4fa1\u683c\u3068\u6bd4\u3079\u3066\u3069\u3046\u306a\u308a\u307e\u3059\u304b\uff1f<br>\u30d2\u30f3\u30c8\uff1a\u57fa\u6e96\u4fa1\u683c\u3092 100 \u30c9\u30eb\u3068\u3057\u3066\u8a08\u7b97\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u554f-6. \u540d\u76ee\u5229\u7387 12% \u3092\u5e74\u8907\u5229\u3067\u904b\u7528\u3057\u305f\u5834\u5408\u3068\u3001\u540d\u76ee\u5229\u7387 11.8% \u3092\u6708\u8907\u5229\u3067\u904b\u7528\u3057\u305f\u5834\u5408\u3067\u306f\u3001\u3069\u3061\u3089\u306e\u6295\u8cc7\u30aa\u30d7\u30b7\u30e7\u30f3\u306e\u65b9\u304c\u30ea\u30bf\u30fc\u30f3\u304c\u9ad8\u3044\u3067\u3059\u304b\uff1f<br>\u30d2\u30f3\u30c8\uff1a\u540c\u4e00\u6761\u4ef6\u3067\u6bd4\u8f03\u3059\u308b\u305f\u3081\u306b\u3001\u6708\u8907\u5229\u30aa\u30d7\u30b7\u30e7\u30f3\u306e\u5b9f\u52b9\u5e74\u5229\u7387\u3092\u8a08\u7b97\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u554f-7.\u30a2\u30f3\u30c6\u30a3\u30fc\u30af\u30ab\u30fc\u306e\u4fa1\u5024\u306f<math data-latex=\"\\$50,000\"><semantics><mrow><mi>$<\/mi><mn>50,000<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\$50,000<\/annotation><\/semantics><\/math>\u3067\u3001\u5e74\u9593<math data-latex=\"8\\%\"><semantics><mrow><mn>8<\/mn><mi>%<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">8\\%<\/annotation><\/semantics><\/math>\u306e\u5272\u5408\u3067\u5024\u4e0a\u304c\u308a\u3059\u308b\u3068\u4e88\u60f3\u3055\u308c\u307e\u3059\u3002$t$\u5e74\u5f8c\u306e\u4fa1\u5024\uff08<math data-latex=\"V\"><semantics><mi>V<\/mi><annotation encoding=\"application\/x-tex\">V<\/annotation><\/semantics><\/math>\uff09\u3092\u30e2\u30c7\u30eb\u5316\u3059\u308b\u5f0f\u306f\u3069\u308c\u3067\u3059\u304b\uff1f<br>\u30d2\u30f3\u30c8\uff1a\u5024\u4e0a\u304c\u308a\u3068\u306f\u3001\u4fa1\u5024\u304c\u6642\u9593\u306e\u7d4c\u904e\u3068\u3068\u3082\u306b\u5897\u52a0\u3059\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u554f-8. 20,000$\u76f8\u5f53\u306e\u6a5f\u68b0\u306e\u300c\u9013\u6e1b\u6cd5\u300d\u6e1b\u4fa1\u511f\u5374\u30e2\u30c7\u30eb\u3067\u306f\u3001\u5e74\u7387<math data-latex=\"15\\%\"><semantics><mrow><mn>15<\/mn><mi>%<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">15\\%<\/annotation><\/semantics><\/math>\u306e\u5272\u5408\u3067\u6e1b\u4fa1\u511f\u5374\u3057\u307e\u3059\u30022\u5e74\u5f8c\u306e\u5e33\u7c3f\u4fa1\u984d\u306f\u3044\u304f\u3089\u3067\u3059\u304b\uff1f<br>\u30d2\u30f3\u30c8\uff1a\u9013\u6e1b\u6cd5\u3068\u306f\u3001\u4fa1\u5024\u304c\u6bce\u5e74(1-r)\u500d\u306b\u306a\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u554f-9. \u9280\u884c\u53e3\u5ea7\u306e\u91d1\u5229\u304c5%\u3067\u3001\u30a4\u30f3\u30d5\u30ec\u7387\u304c3%\u306e\u5834\u5408\u3001\u6295\u8cc7\u306e\u300c\u5b9f\u8cea\u300d\u53ce\u76ca\u7387\u306f\u3044\u304f\u3089\u3067\u3059\u304b\uff1f<br>\u30d2\u30f3\u30c8\uff1a\u91d1\u5229\u306e\u4e0a\u6607\u304b\u3089\u8cfc\u8cb7\u529b\u306e\u4f4e\u4e0b\u3092\u5dee\u3057\u5f15\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u554f-10. \u3042\u308b\u5b66\u751f\u304c4\u5e74\u9593\u306710,000\u30c9\u30eb\u5fc5\u8981\u3067\u3059\u3002\u5e74\u52295%\u306e\u8caf\u84c4\u3092\u6bce\u5e74\u8907\u5229\u3067\u5f97\u3089\u308c\u308b\u5834\u5408\u3001\u4eca\u65e5\u6295\u8cc7\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u91d1\u984d\u306f\u3044\u304f\u3089\u3067\u3057\u3087\u3046\u304b\uff1f\uff08\u7aef\u6570\u306f\u5207\u308a\u6368\u3066\uff09<br>\u30d2\u30f3\u30c8\uff1a\u8907\u5229\u306e\u5f0f A=P(1+r)n \u306b\u304a\u3051\u308b\u300c\u5143\u672c\u300d\uff08P\uff09\u3092\u6c42\u3081\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">*******************<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Right answer<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Q1. D.  $2,700 Using $<math data-latex=\"I = Prt\"><semantics><mrow><mi>I<\/mi><mo>=<\/mo><mi>P<\/mi><mi>r<\/mi><mi>t<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">I = Prt<\/annotation><\/semantics><\/math>$, we calculate <math data-latex=\"\\$10,000 \\times 0.045 \\times 6 = \\$2,700\"><semantics><mrow><mi>$<\/mi><mn>10,000<\/mn><mo>\u00d7<\/mo><mn>0.045<\/mn><mo>\u00d7<\/mo><mn>6<\/mn><mo>=<\/mo><mi>$<\/mi><mn>2,700<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\$10,000 \\times 0.045 \\times 6 = \\$2,700<\/annotation><\/semantics><\/math>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Q2. D. <em>r<\/em>=0.005, <em>n<\/em>=36            The monthly rate is <math data-latex=\"0.06 \/ 12 = 0.005\"><semantics><mrow><mn>0.06<\/mn><mi>\/<\/mi><mn>12<\/mn><mo>=<\/mo><mn>0.005<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">0.06 \/ 12 = 0.005<\/annotation><\/semantics><\/math> and the total periods are <math data-latex=\"3 \\times 12 = 36\"><semantics><mrow><mn>3<\/mn><mo>\u00d7<\/mo><mn>12<\/mn><mo>=<\/mo><mn>36<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">3 \\times 12 = 36<\/annotation><\/semantics><\/math>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Q3. A.  $139.11     Inflation is calculated using the compound interest formula: <math data-latex=\"120 \\times (1 + 0.03)^5 \\approx 139.11\"><semantics><mrow><mn>120<\/mn><mo>\u00d7<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>+<\/mo><mn>0.03<\/mn><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>5<\/mn><\/msup><mo>\u2248<\/mo><mn>139.11<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">120 \\times (1 + 0.03)^5 \\approx 139.11<\/annotation><\/semantics><\/math>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Q4. B.  $1,500                         To find the pre-tax price, divide the total by <math data-latex=\"1.10\"><semantics><mn>1.10<\/mn><annotation encoding=\"application\/x-tex\">1.10<\/annotation><\/semantics><\/math>: <math data-latex=\"\\$1,650 \/ 1.1 = \\$1,500\"><semantics><mrow><mi>$<\/mi><mn>1,650<\/mn><mi>\/<\/mi><mn>1.1<\/mn><mo>=<\/mo><mi>$<\/mi><mn>1,500<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\$1,650 \/ 1.1 = \\$1,500<\/annotation><\/semantics><\/math>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Q5. D.  It is 4% lower than the original price.     Multiplying the growth factors <math data-latex=\"(1.20 \\times 0.80)\"><semantics><mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>1.20<\/mn><mo>\u00d7<\/mo><mn>0.80<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">(1.20 \\times 0.80)<\/annotation><\/semantics><\/math> equals <math data-latex=\"0.96\"><semantics><mn>0.96<\/mn><annotation encoding=\"application\/x-tex\">0.96<\/annotation><\/semantics><\/math>, which is a <math data-latex=\"4\\%\"><semantics><mrow><mn>4<\/mn><mi>%<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">4\\%<\/annotation><\/semantics><\/math> decrease.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Q6. D.   The 11.8% compounded monthly is better.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The effective annual rate is <math data-latex=\"(1 + 0.118\/12)^{12} - 1 \\approx 12.46\\%\"><semantics><mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>+<\/mo><mn>0.118<\/mn><mi>\/<\/mi><mn>12<\/mn><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>12<\/mn><\/msup><mo>\u2212<\/mo><mn>1<\/mn><mo>\u2248<\/mo><mn>12.46<\/mn><mi>%<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">(1 + 0.118\/12)^{12} &#8211; 1 \\approx 12.46\\%<\/annotation><\/semantics><\/math>, which beats <math data-latex=\"12\\%\"><semantics><mrow><mn>12<\/mn><mi>%<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">12\\%<\/annotation><\/semantics><\/math>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Q7. B. <math data-latex=\"V = 50,000(1.08)^t\"><semantics><mrow><mi>V<\/mi><mo>=<\/mo><mn>50,000<\/mn><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>1.08<\/mn><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mi>t<\/mi><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">V = 50,000(1.08)^t<\/annotation><\/semantics><\/math>      Appreciation is modeled by a geometric growth formula where the base is <math data-latex=\"1\"><semantics><mn>1<\/mn><annotation encoding=\"application\/x-tex\">1<\/annotation><\/semantics><\/math> plus the growth rate.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Q8. A.    <math data-latex=\"\\$14,450\"><semantics><mrow><mi>$<\/mi><mn>14,450<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\$14,450<\/annotation><\/semantics><\/math>  The value is calculated as <math data-latex=\"20,000 \\times (1 - 0.15)^2 = 20,000 \\times 0.7225 = \\$14,450\"><semantics><mrow><mn>20,000<\/mn><mo>\u00d7<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mn>0.15<\/mn><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>=<\/mo><mn>20,000<\/mn><mo>\u00d7<\/mo><mn>0.7225<\/mn><mo>=<\/mo><mi>$<\/mi><mn>14,450<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">20,000 \\times (1 &#8211; 0.15)^2 = 20,000 \\times 0.7225 = \\$14,450<\/annotation><\/semantics><\/math>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Q9. C.  2%  The &#8216;real&#8217; rate is approximately the nominal rate minus the inflation rate (<math data-latex=\"5\\% - 3\\% = 2\\%\"><semantics><mrow><mn>5<\/mn><mi>%<\/mi><mo>\u2212<\/mo><mn>3<\/mn><mi>%<\/mi><mo>=<\/mo><mn>2<\/mn><mi>%<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">5\\% &#8211; 3\\% = 2\\%<\/annotation><\/semantics><\/math>)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Q10. A. <math data-latex=\"\\$8,227\"><semantics><mrow><mi>$<\/mi><mn>8,227<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\$8,227<\/annotation><\/semantics><\/math>         This is a Present Value calculation: <math data-latex=\"PV = 10,000 \/ (1.05)^4 \\approx 8227.02\"><semantics><mrow><mi>P<\/mi><mi>V<\/mi><mo>=<\/mo><mn>10,000<\/mn><mi>\/<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>1.05<\/mn><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>4<\/mn><\/msup><mo>\u2248<\/mo><mn>8227.02<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">PV = 10,000 \/ (1.05)^4 \\approx 8227.02<\/annotation><\/semantics><\/math>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><br>   <\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>To prepare you for the rigors of Unit 1 General Mathematics, these warm-up questions focus on the financial modeling skills required for high-achieving students. We will move beyond simple calculations to explore the &#8220;Time Value of Money,&#8221; the impact of compounding periods, and the nuances of inflation. Warm-up: Consumer Arithmetic (General Mathematics) Q-1. An investor [&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-964","post","type-post","status-publish","format-standard","hentry","category-math"],"_links":{"self":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts\/964","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=964"}],"version-history":[{"count":6,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts\/964\/revisions"}],"predecessor-version":[{"id":979,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts\/964\/revisions\/979"}],"wp:attachment":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=964"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=964"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=964"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}