{"id":53941,"date":"2014-06-09T07:20:30","date_gmt":"2014-06-08T23:20:30","guid":{"rendered":"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=53941"},"modified":"2021-10-06T16:18:08","modified_gmt":"2021-10-06T08:18:08","slug":"%e4%b8%83%e4%ba%8c%e6%b3%95%e5%89%87%ef%bc%8d%e8%a4%87%e5%88%a9%e4%bc%b0%e7%ae%97%ef%bc%88the-rule-of-72%ef%bc%89","status":"publish","type":"post","link":"http:\/\/localhost\/%e4%b8%83%e4%ba%8c%e6%b3%95%e5%89%87%ef%bc%8d%e8%a4%87%e5%88%a9%e4%bc%b0%e7%ae%97%ef%bc%88the-rule-of-72%ef%bc%89\/","title":{"rendered":"\u4e03\u4e8c\u6cd5\u5247\uff0d\u8907\u5229\u4f30\u7b97\uff08The Rule of 72\uff09"},"content":{"rendered":"

\u4e03\u4e8c\u6cd5\u5247\uff0d\u8907\u5229\u4f30\u7b97\uff08The Rule of 72\uff09<\/strong><\/span>
\n\u570b\u7acb\u81fa\u7063\u5e2b\u7bc4\u5927\u5b78\u6578\u5b78\u6240\u535a\u58eb\u73ed\u9ec3\u4fca\u744b<\/strong><\/span><\/p>\n

\u7121\u8ad6\u5728\u751f\u6d3b\u4e2d\u6216\u8005\u9032\u884c\u751f\u6daf\u898f\u5283\u3001\u6295\u8cc7\u7406\u8ca1\u6642\uff0c\u5f80\u5f80\u6703\u9047\u5230\u6d89\u53ca\u5229\u7387\u3001\u6295\u8cc7\u5de5\u5177\u7684\u5e73\u5747\u916c\u7387\u6216\u8005\u6210\u9577\u7387\u7b49\u76f8\u95dc\u554f\u984c\uff0c\u53c8\u6216\u8005\u6709\u95dc\u71df\u6536\u6210\u9577\u3001\u7d93\u6fdf\u6210\u9577\u7387\u7b49\u516c\u53f8\u570b\u5bb6\u5927\u4e8b\uff0c\u5728\u5728\u96e2\u4e0d\u958b\u6578\u5b78\u4e2d\u7684\u8907\u5229\u554f\u984c\u3002\u4e5f\u8a31\u4f60\u6703\u597d\u5947\uff0c\u5728\u56fa\u5b9a\u5229\u7387\uff08\u6210\u9577\u7387\uff09\u4e4b\u4e0b\uff0c\u82e5\u5e0c\u671b\u672c\u91d1\u3001\u71df\u6536\u7ffb\u500d\uff0c\u53c8\u6216\u8005\u4e3b\u653f\u8005\u5e0c\u671bGDP (Gross Domestic Product<\/em>\uff0c\u570b\u5167\u751f\u7522\u6bdb\u984d)\u7ffb\u500d\uff0c\u90a3\u9700\u8981\u591a\u5c11\u5e74\u7684\u6642\u9593\u5462\uff1f\u5f9e\u53e6\u4e00\u500b\u65b9\u5411\u8003\u616e\uff0c\u82e5\u5e0c\u671b\u5728\u56fa\u5b9a\u5e74\u9650\u5167\uff08\u4f8b\u598210\u5e74\uff09\u672c\u91d1\u80fd\u7ffb\u500d\uff0c\u90a3\u9ebc\u9700\u8981\u5e73\u5747\u5e74\u6210\u9577\u7387\u591a\u5c11\u7684\u6295\u8cc7\u5de5\u5177\u6216\u8907\u5229\u6548\u679c\u624d\u80fd\u9054\u6210\u6b64\u76ee\u6a19\u5462\uff1f<\/p>\n

\u8209\u4f8b\u4f86\u8aaa\uff0c\u73fe\u6709\u672c\u91d1100\u842c\uff0c\u82e5\u4ee58%\u8907\u5229\u8a08\u7b97\uff0c\u5927\u7d04\u591a\u5c11\u5e74\u6703\u7ffb\u500d\u5462\uff1f\u5728\u5b78\u904e\u4e2d\u5b78\u6307\u5c0d\u6578\u76f8\u95dc\u6578\u5b78\u77e5\u8b58\u8207\u67e5\u5c0d\u8868\u4e4b\u5f8c\uff0c\u8655\u7406\u9019\u500b\u554f\u984c\u4e26\u4e0d\u56f0\u96e3\uff0c\u9996\u5148\u6211\u5011\u5047\u8a2d\u672c\u91d1\u70ba100\uff08\u842c\uff09\uff0c\u4ee58%\u8907\u5229\u8a08\u7b97\uff0c\u4e26\u5047\u8a2dn<\/i>\u671f\u5f8c\u672c\u91d1\u7ffb\u500d\uff0c\u5247\u53ef\u5f97\u4e0b\u5f0f\uff1a<\/p>\n

\\(200=100(1+\\frac{8}{100})^n\\)<\/p>\n

\u6b64\u5f0f\u5373\u76f8\u7576\u65bc\u6c42\u89e3\u6307\u6578\u65b9\u7a0b\u5f0f\uff1a<\/p>\n

\\(2=(1+\\frac{8}{100})^n\\)<\/p>\n

\u5169\u908a\u53d6\u5e38\u7528\u5c0d\u6578\uff0c\u4e26\u4f9d\u5c0d\u6578\u5f8b\u53ef\u5f97\uff1a<\/p>\n

\\(\\log 2=n\\log 1.08\\)<\/p>\n

\u4f9d\u76f8\u95dc\u5c0d\u6578\u5f8b\u4ee5\u53ca\u67e5\u8868\u53ef\u5f97\uff1a<\/p>\n

\\(0.301 \\approx n\\log 1.08 \\approx n \\cdot 0.0334\\)<\/p>\n

\u5982\u6b64\u53ef\u5f97\u00a0\\(n \\approx \\frac{{0.301}}{{0.0334}} \\approx 0.901\\)\uff0c\u4ea6\u5373\u7d04\u4e5d\u671f\u5f8c\u672c\u91d1\u6703\u7ffb\u500d\u3002<\/p>\n

\u4ee5\u4e0b\u518d\u8209\u4e00\u4f8b\u8aaa\u660e\uff0c\u5047\u8a2d\u67d0\u516c\u53f8\u4eca\u5e74\u7684\u5e74\u71df\u6536\u70ba100\u5104\uff0c\u5018\u82e5\u516c\u53f8\u5e0c\u671b\u572812\u5e74\u5f8c\u80fd\u7ffb\u500d\uff08\u5373\u5e74\u71df\u6536\u9054200\u5104\uff09\uff0c\u5247\u6240\u9700\u5e73\u5747\u5e74\u6210\u9577\u7387\u7d04\u70ba\u591a\u5c11\u5462\uff1f\u9019\u88e1\u6211\u5011\u5df2\u77e5\u8a72\u516c\u53f8\u4eca\u5e74\u7684\u5e74\u71df\u6536\u70ba100\uff08\u5104\uff09\uff0c\u5e73\u5747\u5e74\u6210\u9577\u7387r<\/i> %\uff0c\u82e512\u5e74\u5f8c\u71df\u6536\u7ffb\u500d\uff0c\u5247\u53ef\u5f97\u4e0b\u5f0f\uff1a<\/p>\n

\\(200 = 100{(1 + \\frac{r}{{100}})^{12}}\\)<\/p>\n

\u6b64\u5f0f\u5373\u76f8\u7576\u65bc\u4e0b\u8ff0\u65b9\u7a0b\u5f0f\uff1a<\/p>\n

\\(2={(1 + \\frac{r}{{100}})^{12}}\\)<\/p>\n

\u5169\u908a\u53d6\u5e38\u7528\u5c0d\u6578\uff0c\u4e26\u4f9d\u5c0d\u6578\u5f8b\u53ef\u5f97\uff1a<\/p>\n

\\(\\log 2 = 12\\log (1 + \\frac{r}{{100}})\\)<\/p>\n

\\(\\log (1 + \\frac{r}{{100}}) \\approx \\frac{{0.301}}{{12}} \\approx 0.02508\\)<\/p>\n

\u67e5\u8868\u53ef\u77e5\u5927\u7d04\u9700\u89816\u5e74\u7684\u6642\u9593\u3002<\/p>\n

\u5f9e\u4ee5\u4e0a\u5169\u500b\u4f8b\u5b50\u7684\u7d50\u8ad6\u4f86\u770b\uff1a<\/p>\n

\\(8\\%\\) \u8907\u5229\uff0c\u7d93 \\(9\\) \u5e74\u5f8c\u7ffb\u500d\u3002<\/p>\n

\\(12\\) \u5e74\u5f8c\u7ffb\u500d\uff0c\u9700 \\(6\\%\\) \u7684\u9577\u6210\u7387\u3002<\/p>\n

\u6709\u6c92\u6709\u767c\u73fe\u4ec0\u9ebc\u6a23\u6709\u8da3\u7684\u95dc\u4fc2\u5462\uff1f\u4e5f\u8a31\u4f60\u5df2\u5f9e\u4e0a\u9762\u7684\u4f8b\u5b50\u89c0\u5bdf\u51fa\uff1a<\/p>\n

\\(8\\cdot 9=72;12\\cdot 6=72\\)<\/p>\n

\u9019\u88e1\u7684 \\(72\\) \u662f\u5de7\u5408\u55ce\uff1f\u4e8b\u5be6\u4e0a\uff0c\u300c\\(72\\)\u300d\u6b63\u662f\u6211\u5011\u7684\u7d93\u6fdf\u5b78\u4e0a\u7528\u4f86\u4f30\u7b97\u8907\u5229\u6548\u679c\u7684\u4e00\u500b\u9b54\u8853\u6578\u5b57<\/b>\u3002\u4e00\u822c\u800c\u8a00\uff0c\u7d93\u6fdf\u5b78\u4e0a\u6709\u4e00\u500b\u5e38\u7528\u4e14\u76f8\u7576\u5be6\u7528\u7684\u4e03\u4e8c\u6cd5\u5247<\/b>\uff0c\u53ef\u4ee5\u5e6b\u52a9\u6211\u5011\u5c0d\u8907\u5229\u6548\u679c\u4f5c\u4e00\u7c21\u55ae\u7684\u4f30\u7b97\uff0c\u4f30\u7b97\u51fa\u672c\u91d1\u500d\u589e\u6240\u9700\u7684\u6642\u9593\u6216\u6240\u9700\u4e4b\u5229\u7387\u3002\u6240\u8b02\u7684\u4e03\u4e8c\u6cd5\u5247\u5982\u4e0b\uff1a<\/p>\n

\u8a2d\u672c\u91d1\u70ba \\(M\\)\u3001\u82e5\u4ee5\u8907\u5229\u8a08\u7b97\uff0c\u5df2\u77e5\u5229\u7387\uff08\u6210\u9577\u7387\uff09\u70ba \\(r\\%\\)\uff0c\u5247\u671f\u6578 \\(n\\)\uff08\\(n\\) \u70ba\u81ea\u7136\u6578\uff09\u6eff\u8db3 \\(n\\cdot r=72\\)\u00a0<\/i>\u6642\uff0c\u672c\u91d1\u7d04\u6703\u7ffb\u500d\uff0c\u5373\u672c\u5229\u548c\u7d04\u6210\u9577\u70ba \\(2M\\)\u3002<\/b><\/p>\n

\u8209\u4f8b\u4f86\u8aaa\uff0c\u672c\u91d1100\u842c\u5143\uff0c\u82e5\u4ee53%\u8907\u5229\u8a08\u7b97\uff0c\u5247\u7d0424\u671f\u5f8c\uff0c\u6703\u8b8a\u6210200\u842c\u5143\uff1b\u82e5\u4ee54%\u8907\u5229\u8a08\u7b97\uff0c\u5247\u7d04\u757618\u671f\u5f8c\uff0c\u8b8a\u6210200\u842c\u5143\u3002\u63db\u500b\u89d2\u5ea6\u60f3\uff0c\u6295\u8cc7\u6642\uff0c\u82e5\u5e0c\u671b\u672c\u91d1\u57289\u5e74\u5167\u7ffb\u500d\uff0c\u5247\u9700\u8981\u5e74\u5316\u5831\u916c\u73878%\u7684\u6295\u8cc7\u5de5\u5177\uff0c\u4ee5\u6b64\u985e\u63a8\uff0c\u4fbf\u53ef\u5728\u56fa\u5b9a\u5229\u7387\uff08\u6210\u9577\u7387\uff09\u7684\u689d\u4ef6\u4e0b\uff0c\u4f30\u7b97\u51fa\u7ffb\u500d\u6240\u9700\u7684\u671f\u6578\uff0c\u53c8\u6216\u8005\u5728\u56fa\u5b9a\u7684\u671f\u6578\u9650\u5236\u4e0b\uff0c\u4f30\u7b97\u51fa\u7ffb\u500d\u6240\u9700\u7684\u5229\u7387\uff08\u6210\u9577\u7387\uff09\u3002<\/p>\n

\u6700\u5f8c\uff0c\u6211\u5011\u8a66\u5229\u7528\u76f8\u95dc\u51fd\u6578\u5716\u5f62\u4f86\u4f5c\u7c21\u55ae\u8aaa\u660e\u3002\u9996\u5148\u8a2d\u672c\u91d1\u70ba \\(M\\)\u3001\u82e5\u4ee5 \\(x\\%\\)\u00a0\u7684\u8907\u5229\uff08\u6210\u9577\u7387\uff09\u8a08\u7b97\uff0c\u8a2d\u671f\u6578\u70ba \\(y\\)\uff08\\(y\\)\u00a0<\/i>\u70ba\u81ea\u7136\u6578\uff09\u6642\uff0c\u672c\u91d1\u7ffb\u500d\uff0c\u5373\u672c\u5229\u548c\u7d04\u70ba\u539f\u672c\u7684 \\(2\\) \u500d \\(2M\\)\u3002\u53ef\u5f97\u4e0b\u5f0f\uff1a<\/p>\n

\\(2M = M{(1 + x)^y}\\)<\/p>\n

\u5373 \\(2=(1+x)^y\\)\uff0c\u5247 \\(\\log 2=y\\log(1+x)\\)\uff0c\u53ef\u5f97\u4e00\u51fd\u6578 \\(y = \\frac{{\\log 2}}{{\\log (1 + x)}}\\)\uff0c\u63a5\u8457\u4f5c\u6b64\u51fd\u6578\u7684\u5716\u5f62\uff08\u5982\u5716\u4e00\u6240\u793a\uff09\uff0c\u6b64\u51fd\u6578\u7684\u5716\u5f62\u7684\u6a6b\u5750\u6a19\u70ba\u5229\u7387\uff0c\u7e31\u5750\u6a19\u70ba\u671f\u6578\u3002\u5f9e\u5716\u4e2d\u53ef\u4ee5\u770b\u51fa\u7576\u5229\u738718%\u6642\uff0c\u7d044\u671f\u53ef\u9054\u6210\u7ffb\u500d\uff1b\u7576\u5229\u73879%\u6642\uff0c\u7d048\u671f\u53ef\u9054\u6210\u7ffb\u500d\uff1b\u7576\u5229\u73878%\u6642\uff0c\u7d049\u671f\u53ef\u9054\u6210\u7ffb\u500d\uff1b\u7576\u5229\u73876%\u6642\uff0c\u7d0412\u671f\u53ef\u9054\u6210\u7ffb\u500d\uff1b\u5e0c\u671b7\u671f\u5f8c\u9054\u6210\u7ffb\u500d\uff0c\u5247\u5229\u7387\u7d04\u970010%\uff1b\u5e0c\u671b12\u671f\u9054\u6210\u7ffb\u500d\uff0c\u5247\u5229\u7387\u7d04\u97006%\u3002<\/p>\n

\"53941_p1\"<\/a>

\u5716\u4e00 \\(y=\\frac{\\log 2}{\\log(1+x)}\\) \u4e4b\u51fd\u6578\u5716<\/p><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"

\u4e03\u4e8c\u6cd5\u5247\uff0d\u8907\u5229\u4f30\u7b97\uff08The Rule of 72\uff09 \u570b\u7acb\u81fa\u7063\u5e2b\u7bc4\u5927\u5b78\u6578\u5b78\u6240\u535a\u58eb\u73ed\u9ec3\u4fca\u744b \u7121\u8ad6\u5728\u751f\u6d3b\u4e2d\u6216\u8005\u9032\u884c\u751f…<\/p>\n","protected":false},"author":50,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[111,236],"tags":[6637,6638,486],"class_list":["post-53941","post","type-post","status-publish","format-standard","hentry","category-mathematics00","category-math10","tag-6637","tag-6638","tag-486","loop-entry","cat-111","cat-236","no-thumbnail"],"views":5394,"_links":{"self":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/53941","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/users\/50"}],"replies":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/comments?post=53941"}],"version-history":[{"count":1,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/53941\/revisions"}],"predecessor-version":[{"id":87034,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/53941\/revisions\/87034"}],"wp:attachment":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/media?parent=53941"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/categories?post=53941"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/tags?post=53941"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}