Problem 56120. Compound Interest : Compounding Periods

Created by Mehmet OZC

Solve Later

{"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 : Compound Interest</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 = P(1+r)^n</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 at the end of n periods</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>P : Present 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>r : Annual nominal rate</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 : Total number of compounding periods</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, P 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: 213.741px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 106.87px; transform-origin: 406.997px 106.87px; 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 : Compound Interest</span></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="vertical-align:-5px"><img src="data:image/png;base64,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" width="89" height="19.5" style="width: 89px; height: 19.5px;"></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 at the end of n periods</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="">P : Present 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="">r : Annual nominal rate</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 : Total number of compounding periods</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, P and r. </span></span></div></div></div>

Solve

Solution Stats

25 Solutions
19 Solvers

Last Solution submitted on Dec 05, 2022

Last 200 Solutions

Problem Recent Solvers19

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 56120. Compound Interest : Compounding Periods

Solution Stats

Last 200 Solutions

Problem Recent Solvers19

Suggested Problems

More from this Author92

Problem Tags

Community Treasure Hunt

Problem 56120. Compound Interest : Compounding Periods

Solution Stats

Last 200 Solutions

Problem Recent Solvers19

Suggested Problems

More from this Author92

Problem Tags

Community Treasure Hunt

Players