Problem 56140. Ordinary Annuity : Number of payments (Future Value)

Created by Mehmet OZC

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{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Theorem : Future Value of an Ordinary Annuity </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>F = A \\frac{(1+r)^n -1}{r}</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>where;</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>F : Future value</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>A : Periodic payment</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>r : Rate per period</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>n : Number of periods (payments)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Calculate n, given, F, A and r. </w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div 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; "><div 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; "><div 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; "><span 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; "><span style="">Theorem : Future Value of an Ordinary Annuity </span></span></div><div 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; "><span style="vertical-align:-15px"><img src="data:image/png;base64,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" width="117.5" height="36.5" style="width: 117.5px; height: 36.5px;"></span></div><div 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; "><span 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; "><span style="">where;</span></span></div><ul 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; "><li 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; "><span style="block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">F : Future value</span></span></li><li 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; "><span style="block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">A : Periodic payment</span></span></li><li 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; "><span style="block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">r : Rate per period</span></span></li><li 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; "><span style="block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">n : Number of periods (payments)</span></span></li></ul><div 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; "><span 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; "><span style="">Calculate n, given, F, A and r. </span></span></div></div></div>

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Problem 56140. Ordinary Annuity : Number of payments (Future Value)

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Problem 56140. Ordinary Annuity : Number of payments (Future Value)

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