Problem 56135. Ordinary Annuity : Rate (Future Value)

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 : 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 r, given, F, A and n. Assume interest rate is a positive real number. </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: 20.4333px; 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; "><div style="block-size: 229.233px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 114.617px; transform-origin: 407px 114.617px; vertical-align: baseline; "><div 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; "><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: 150px 8px; transform-origin: 150px 8px; unicode-bidi: normal; "><span style="">Theorem : Future Value of an Ordinary Annuity </span></span></div><div style="block-size: 36.5px; 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 18.25px; text-align: left; transform-origin: 384px 18.25px; 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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" style="width: 117.5px; height: 36.5px;" width="117.5" height="36.5"></span></div><div 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; "><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: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; "><span style="">where;</span></span></div><ul style="block-size: 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; "><li 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; "><span style="block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 50.5px 8px; transform-origin: 50.5px 8px; unicode-bidi: normal; "><span style="">F : Future value</span></span></li><li 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; "><span style="block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 65px 8px; transform-origin: 65px 8px; unicode-bidi: normal; "><span style="">A : Periodic payment</span></span></li><li 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; "><span style="block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 58px 8px; transform-origin: 58px 8px; unicode-bidi: normal; "><span style="">r : Rate per period</span></span></li><li 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; "><span 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; "><span style="">n : Number of periods (payments)</span></span></li></ul><div 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; "><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: 242px 8px; transform-origin: 242px 8px; unicode-bidi: normal; "><span style="">Calculate r, given, F, A and n. Assume interest rate is a positive real number. </span></span></div></div></div>

Solve

Solution Stats

26 Solutions
14 Solvers

Last Solution submitted on Nov 11, 2022

Last 200 Solutions

Problem Comments

5 Comments

5 Comments

Show 2 older comments

William on 1 Oct 2022

The "correct" values of r used in these tests all appear to have errors greater than the tolerance of 1e-4, as you can verify by plugging them in to the formula for Future Value.

Mehmet OZC on 1 Oct 2022

Thanks for the catch. I have updated the test suite.

William on 1 Oct 2022

Thanks Mehmet, but there are still big errors. The correct answers are:
Test 1: r = 0.08837372469
Test 2: r = 0.06774487509
Test 3: r = 0.01422142597

Mehmet OZC on 1 Oct 2022

I fixed the errors. I also updated the assert statements.

Rafael S.T. Vieira on 3 Nov 2022

Good problem.

Problem Recent Solvers14

Problem Tags

Community Treasure Hunt

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

Start Hunting!

Problem 56135. Ordinary Annuity : Rate (Future Value)

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers14

Suggested Problems

More from this Author92

Problem Tags

Community Treasure Hunt

Problem 56135. Ordinary Annuity : Rate (Future Value)

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers14

Suggested Problems

More from this Author92

Problem Tags

Community Treasure Hunt

Players