{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-16T00:12:35.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-16T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":56140,"title":"Ordinary Annuity : Number of payments (Future Value)","description":"Theorem : Future Value of an Ordinary Annuity \r\n\r\nwhere;\r\nF : Future value\r\nA : Periodic payment\r\nr : Rate per period\r\nn : Number of periods (payments)\r\nCalculate n, given, F, A and r. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 229.056px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 114.522px; transform-origin: 406.997px 114.528px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Future Value of an Ordinary Annuity \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.3166px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 18.1526px; text-align: left; transform-origin: 383.996px 18.1583px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"117.5\" height=\"36.5\" style=\"width: 117.5px; height: 36.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eF : Future value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (payments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate n, given, F, A and r. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = annuityFMaturity(F,A,r)\r\n\r\nend","test_suite":"%%\r\nF = 500000;\r\nA = 10000;\r\nr = 0.085\r\nn = 20.33;\r\nassert(abs(annuityFMaturity(F,A,r) - n) \u003c= 1e-2)\r\n\r\n%%\r\nF = 100;\r\nA = 1;\r\nr = 0.074\r\nn = 29.81;\r\nassert(abs(annuityFMaturity(F,A,r) - n) \u003c= 1e-2)\r\n\r\n\r\n%%\r\nF = 1000;\r\nA = 0.1;\r\nr = 0.052\r\nn = 123.40;\r\nassert(abs(annuityFMaturity(F,A,r) - n )\u003c= 1e-2)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:30:39.000Z","deleted_by":null,"deleted_at":null,"solvers_count":30,"test_suite_updated_at":"2022-10-01T16:30:39.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T07:39:23.000Z","updated_at":"2026-02-17T09:03:03.000Z","published_at":"2022-09-30T16:54:47.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Future Value of an Ordinary Annuity \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF = A \\\\frac{(1+r)^n -1}{r}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF : Future value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA : Periodic payment\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Rate per period\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Number of periods (payments)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate n, given, F, A and r. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56165,"title":"Ordinary Annuity : Number of Payments (Present Value)","description":"Theorem : Present Value of an Ordinary Annuity\r\n\r\nwhere;\r\nP : Present value of all payments\r\nA : Periodic payment\r\nr : Interest rate per period\r\nn : Number of periods (peyments)\r\nCalculate n, given P, A and r. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 230.733px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 115.367px; transform-origin: 407px 115.367px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 151.5px 8px; transform-origin: 151.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTheorem : Present Value of an Ordinary Annuity\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 38px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 19px; text-align: left; transform-origin: 384px 19px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg 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81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 40.8667px; transform-origin: 391px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 103.5px 8px; transform-origin: 103.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eP : Present value of all payments\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 65px 8px; transform-origin: 65px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 81px 8px; transform-origin: 81px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003er : Interest rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 105.5px 8px; transform-origin: 105.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (peyments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.5px 8px; transform-origin: 92.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate n, given P, A and r. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = annuityPMaturity(P,A,r)\r\n \r\nend","test_suite":"%%\r\nP = 1200;\r\nA = 500;\r\nr = 0.05;\r\nn = 2.62;\r\nassert(abs(annuityPMaturity(P,A,r) - n )\u003c= 1e-2)\r\n\r\n%%\r\nP = 10000;\r\nA = 1500;\r\nr = 0.0075;\r\nn = 6.86;\r\nassert(abs(annuityPMaturity(P,A,r) - n) \u003c= 1e-2)\r\n\r\n\r\n%%\r\nP = 400;\r\nA = 20;\r\nr = 0.0025;\r\nn = 20.54;\r\nassert(abs(annuityPMaturity(P,A,r) - n) \u003c= 1e-2)\r\n\r\n%%\r\nP = randi(10)*1e3;\r\nA = 2*P;\r\nr = 1;\r\nn = 1;\r\nassert(abs(annuityPMaturity(P,A,r) - n) \u003c= 1e-2)\r\n\r\n%%\r\nP = randi(10)*3e3;\r\nA = 4*P/3;\r\nr = 1;\r\nn = 2;\r\nassert(abs(annuityPMaturity(P,A,r) - n) \u003c= 1e-2)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":223089,"edited_at":"2022-12-19T07:56:40.000Z","deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":"2022-12-19T07:56:40.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T16:36:30.000Z","updated_at":"2026-02-18T10:17:09.000Z","published_at":"2022-09-30T16:53:13.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Present Value of an Ordinary Annuity\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP = A \\\\frac{(1+r)^n-1}{r (1+r)^n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc 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height: 36.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eF : Future value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (payments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate n, given, F, A and r. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = annuityFMaturity(F,A,r)\r\n\r\nend","test_suite":"%%\r\nF = 500000;\r\nA = 10000;\r\nr = 0.085\r\nn = 20.33;\r\nassert(abs(annuityFMaturity(F,A,r) - n) \u003c= 1e-2)\r\n\r\n%%\r\nF = 100;\r\nA = 1;\r\nr = 0.074\r\nn = 29.81;\r\nassert(abs(annuityFMaturity(F,A,r) - n) \u003c= 1e-2)\r\n\r\n\r\n%%\r\nF = 1000;\r\nA = 0.1;\r\nr = 0.052\r\nn = 123.40;\r\nassert(abs(annuityFMaturity(F,A,r) - n )\u003c= 1e-2)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:30:39.000Z","deleted_by":null,"deleted_at":null,"solvers_count":30,"test_suite_updated_at":"2022-10-01T16:30:39.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T07:39:23.000Z","updated_at":"2026-02-17T09:03:03.000Z","published_at":"2022-09-30T16:54:47.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Future Value of an Ordinary Annuity \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF = A \\\\frac{(1+r)^n -1}{r}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF : Future value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA : Periodic payment\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Rate per period\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Number of periods (payments)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate n, given, F, A and r. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56165,"title":"Ordinary Annuity : Number of Payments (Present Value)","description":"Theorem : Present Value of an Ordinary Annuity\r\n\r\nwhere;\r\nP : Present value of all payments\r\nA : Periodic payment\r\nr : Interest rate per period\r\nn : Number of periods (peyments)\r\nCalculate n, given P, A and r. 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81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 40.8667px; transform-origin: 391px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 103.5px 8px; transform-origin: 103.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eP : Present value of all payments\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 65px 8px; transform-origin: 65px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 81px 8px; transform-origin: 81px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003er : Interest rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 105.5px 8px; transform-origin: 105.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (peyments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.5px 8px; transform-origin: 92.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate n, given P, A and r. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = annuityPMaturity(P,A,r)\r\n \r\nend","test_suite":"%%\r\nP = 1200;\r\nA = 500;\r\nr = 0.05;\r\nn = 2.62;\r\nassert(abs(annuityPMaturity(P,A,r) - n )\u003c= 1e-2)\r\n\r\n%%\r\nP = 10000;\r\nA = 1500;\r\nr = 0.0075;\r\nn = 6.86;\r\nassert(abs(annuityPMaturity(P,A,r) - n) \u003c= 1e-2)\r\n\r\n\r\n%%\r\nP = 400;\r\nA = 20;\r\nr = 0.0025;\r\nn = 20.54;\r\nassert(abs(annuityPMaturity(P,A,r) - n) \u003c= 1e-2)\r\n\r\n%%\r\nP = randi(10)*1e3;\r\nA = 2*P;\r\nr = 1;\r\nn = 1;\r\nassert(abs(annuityPMaturity(P,A,r) - n) \u003c= 1e-2)\r\n\r\n%%\r\nP = randi(10)*3e3;\r\nA = 4*P/3;\r\nr = 1;\r\nn = 2;\r\nassert(abs(annuityPMaturity(P,A,r) - n) \u003c= 1e-2)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":223089,"edited_at":"2022-12-19T07:56:40.000Z","deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":"2022-12-19T07:56:40.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T16:36:30.000Z","updated_at":"2026-02-18T10:17:09.000Z","published_at":"2022-09-30T16:53:13.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Present Value of an Ordinary Annuity\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP = A \\\\frac{(1+r)^n-1}{r (1+r)^n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc 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