Problem 56065. Easy Sequences 74: Fibonacci Bank Account

Created by Ramon Villamangca

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>In fantasy world where money does grow on trees, a man decided to top-up his bank account, daily. On the first day he noticed that he has initial \"integer\" balance of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>b_1</w:t></w:r></w:customXml><w:r><w:t>, so he made his first \"integer\" deposit of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>d_1</w:t></w:r></w:customXml><w:r><w:t>. On the next days, he made deposit equivalent to the day's starting balance plus the amount he deposited on the previous day. This means that on any </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>k</w:t></w:r></w:customXml><w:r><w:t>-th day the following formula for the amount he would deposit, holds: </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>d_k = b_k+d_{k-1}</w:t></w:r></w:customXml><w:r><w:t>.</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:rPr><w:b/></w:rPr><w:t>Given that on the </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>-th day, he made a deposit of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>d_n</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, calculate his initial balance </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>b_1</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>,</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>his first deposit </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>d_1</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, and his final ending balance at the end of the </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>-th day transaction. </w:t></w:r><w:r><w:t>It is also known that the first deposit he made (</w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>d_1</w:t></w:r></w:customXml><w:r><w:t>) is the smallest possible first deposit to attain </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>d_n</w:t></w:r></w:customXml><w:r><w:t> at the </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t>-th day, using the above formula.</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>While the account balances can be negative, deposits are always positive (no withdrawals please).</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>For example, bank statements if </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n=5</w:t></w:r></w:customXml><w:r><w:t> and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>d_n=50</w:t></w:r></w:customXml><w:r><w:t>, are shown below.</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t> His first deposit </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>d_1=20</w:t></w:r></w:customXml><w:r><w:t>, is the smallest possible first deposit to attain a deposit of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>50</w:t></w:r></w:customXml><w:r><w:t> on the </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>5</w:t></w:r></w:customXml><w:r><w:t>-th day. </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>His starting balance should be </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>-30</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>,</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>and his ending balance at </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>5</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>-th day should be </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>80</w:t></w:r></w:customXml><w:r><w:t>. </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> </w:t></w:r><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"89\"/><w:attr w:name=\"width\" w:val=\"294\"/><w:attr w:name=\"verticalAlign\" w:val=\"baseline\"/><w:attr w:name=\"altText\" w:val=\"\"/><w:attr w:name=\"relationshipId\" w:val=\"rId1\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Since this problem involves unbelievable sums of money,</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t> please reduce your answer modulo </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>2178309</w:t></w:r></w:customXml><w:r><w:t>. Therefore for the above example the final answer should be:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ >> k = mod([-30,20,80],2178309)\n k =\n 2178279 20 80]]></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:rPr><w:b/></w:rPr><w:t>HINT</w:t></w:r><w:r><w:t>: Use of a big integer arithmetic implementation, is not required in this problem. You can get the modulus using </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Pisano_period\"><w:r><w:t>Pisano Period</w:t></w:r></w:hyperlink><w:r><w:t>. </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>2178309</w:t></w:r></w:customXml><w:r><w:t> is the </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>32</w:t></w:r></w:customXml><w:r><w:t>-nd </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Fibonacci_number\"><w:r><w:t>Fibonacci number.</w:t></w:r></w:hyperlink><w:r><w:t> Also, the ratio of the day's ending balance to the deposit approaches the </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Golden_ratio\"><w:r><w:t>Golden Ratio</w:t></w:r></w:hyperlink><w:r><w:t> as the values of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t> gets larger. </w:t></w:r></w:p></w:body></w:document>","relationship":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/image","target":"/media/image1.png","relationshipId":"rId1"}]},{"partUri":"/media/image1.png","contentType":"image/png","content":"data:image/png;base64,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","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: 20.45px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 12.6px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 522.45px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 261.225px; transform-origin: 407px 261.225px; vertical-align: baseline; "><div style="block-size: 77.4px; 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 38.7px; text-align: left; transform-origin: 384px 38.7px; 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: 380.5px 7px; transform-origin: 380.5px 7px; unicode-bidi: normal; ">In fantasy world where money does grow on trees, a man decided to top-up his bank account, daily. On the first day he noticed that he has initial "integer" balance of <img src="data:image/png;base64,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" style="width: 14px; height: 18.5px;" width="14" height="18.5"><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: 119.5px 7px; transform-origin: 119.5px 7px; unicode-bidi: normal; ">, so he made his first "integer" deposit of <img src="data:image/png;base64,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" style="width: 14px; height: 18.5px;" width="14" height="18.5"><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: 146px 7px; transform-origin: 146px 7px; unicode-bidi: normal; ">. On the next days, he made deposit equivalent to the day's starting balance plus the amount he deposited on the previous day. This means that on any k<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: 82.5px 7px; transform-origin: 82.5px 7px; unicode-bidi: normal; ">-th day the following formula for the amount he would deposit, holds: <img src="data:image/png;base64,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" style="width: 79px; height: 18.5px;" width="79" height="18.5"><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: 2px 7px; transform-origin: 2px 7px; unicode-bidi: normal; ">.</div><div style="block-size: 59.4px; 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 29.7px; text-align: left; transform-origin: 384px 29.7px; 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: 56.5px 7px; transform-origin: 56.5px 7px; unicode-bidi: normal; ">Given that on the n<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: 94px 7px; transform-origin: 94px 7px; unicode-bidi: normal; ">-th day, he made a deposit of <img src="data:image/png;base64,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" style="width: 14px; height: 18.5px;" width="14" height="18.5"><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: 95.5px 7px; transform-origin: 95.5px 7px; unicode-bidi: normal; ">, calculate his initial balance <img src="data:image/png;base64,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" style="width: 14px; height: 18.5px;" width="14" height="18.5"><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: 2px 7px; transform-origin: 2px 7px; unicode-bidi: normal; ">,<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: 2px 7px; transform-origin: 2px 7px; unicode-bidi: normal; "> <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: 49.5px 7px; transform-origin: 49.5px 7px; unicode-bidi: normal; ">his first deposit <img src="data:image/png;base64,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" style="width: 14px; height: 18.5px;" width="14" height="18.5"><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: 45px 7px; transform-origin: 45px 7px; unicode-bidi: normal; ">, and his final ending balance at the end of the n<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: 62.5px 7px; transform-origin: 62.5px 7px; unicode-bidi: normal; ">-th day transaction. <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: 135.5px 7px; transform-origin: 135.5px 7px; unicode-bidi: normal; ">It is also known that the first deposit he made (<img src="data:image/png;base64,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" style="width: 14px; height: 18.5px;" width="14" height="18.5"><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: 48.5px 7px; transform-origin: 48.5px 7px; unicode-bidi: normal; ">) is the smallest possible first deposit to attain <img src="data:image/png;base64,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" style="width: 14px; height: 18.5px;" width="14" height="18.5"><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: 20.5px 7px; transform-origin: 20.5px 7px; unicode-bidi: normal; "> at the n<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: 93.5px 7px; transform-origin: 93.5px 7px; unicode-bidi: normal; ">-th day, using the above formula.</div><div style="block-size: 18.9px; 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 9.45px; text-align: left; transform-origin: 384px 9.45px; 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: 284px 7px; transform-origin: 284px 7px; unicode-bidi: normal; ">While the account balances can be negative, deposits are always positive (no withdrawals please).</div><div style="block-size: 57.6px; 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 28.8px; text-align: left; transform-origin: 384px 28.8px; 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: 95.5px 7px; transform-origin: 95.5px 7px; unicode-bidi: normal; ">For example, bank statements if <img src="data:image/png;base64,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" style="width: 33px; height: 16px;" width="33" height="16"><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: 14.5px 7px; transform-origin: 14.5px 7px; unicode-bidi: normal; "> and <img src="data:image/png;base64,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" style="width: 44px; height: 18.5px;" width="44" height="18.5"><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: 53.5px 7px; transform-origin: 53.5px 7px; unicode-bidi: normal; ">, are shown below.<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: 52px 7px; transform-origin: 52px 7px; unicode-bidi: normal; "> His first deposit <img src="data:image/png;base64,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" style="width: 44px; height: 18.5px;" width="44" height="18.5"><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: 87px 7px; transform-origin: 87px 7px; unicode-bidi: normal; ">, is the smallest possible first deposit to attain a deposit of <img src="data:image/png;base64,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" style="width: 16px; height: 16px;" width="16" height="16"><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: 22px 7px; transform-origin: 22px 7px; unicode-bidi: normal; "> on the 5<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: 23.5px 7px; transform-origin: 23.5px 7px; unicode-bidi: normal; ">-th day. <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: 97.5px 7px; transform-origin: 97.5px 7px; unicode-bidi: normal; ">His starting balance should be <img src="data:image/png;base64,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" style="width: 25.5px; height: 16px;" width="25.5" height="16"><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: 2px 7px; transform-origin: 2px 7px; unicode-bidi: normal; ">,<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: 2px 7px; transform-origin: 2px 7px; unicode-bidi: normal; "> <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: 84.5px 7px; transform-origin: 84.5px 7px; unicode-bidi: normal; ">and his ending balance at 5<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: 23.5px 7px; transform-origin: 23.5px 7px; unicode-bidi: normal; ">-th day should be <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACAAAAAgCAYAAABzenr0AAACHUlEQVRYR+1WuUoEQRTc/QIRjcRAPAIjDTwSFUw8P0DFxEDwAkMFTVXQQEHE4wM8NjXwSgzUSAONDDwwECOPT9Aq6Ac9b97MrLCwG0xD0Uxfr7q63mOymSK3bJHjZ1ICJa9ABTzS6HzyiP4rT8/UYl0V8AG8xu2JUqADmzaAF2ALqAaWgBywHkNkAHObbt0N+lkXfB79g0XEItCEhffACrDobeKtSGgHmDYOG8bYobHvFmN1QLdFwiKwjYVTwCBwogKd4bsNaFAq8KmegHKgWQUSYucYH9XqWQQYpBeYBPYMApyrVAdN4HvXKVSv9pDcpxvrRH/tz1sElrFgwR3Wg15MJAfxJn0qCGVuAaKe5xlzfAb9rGYh4lvfOTnZjwPvAJWhxO1aRnz/OkKhAG5cVOV5rUkKcJ5GvHQBf9B/O1IzRnBf4oIREBLMBmnMgDEg8Ib4Zspe5akAlwX8E1UHeKt9gIZi7tMTbFSDKXjkEZO05VCSAlwTiBlFQHJX0o23PAboAZLQOV1QD0hKsXqteTf1c127nR4huSQFQhkUVwesQiTktJuleFkpyjsIwVBt+S8BMZwOJOM0qk5TKeEhA4YM4eSW0mkVFZmLq5JauTmcuxr1PFEmFElHPMfzJhcA5ScR3egRFhy2IYAVVOoJ91l7Yn/JKGu/M9cb+jLgFNB1QBNhoC6Ae2qAg7g9Jf9HZChd2KFUgVSBVIFUgT/GIIchImHTvwAAAABJRU5ErkJggg==" style="width: 16px; height: 16px;" width="16" height="16"><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: 4px 7px; transform-origin: 4px 7px; unicode-bidi: normal; ">. </div><div style="block-size: 94.45px; 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 47.225px; text-align: left; transform-origin: 384px 47.225px; 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: 48px 7px; transform-origin: 48px 7px; unicode-bidi: normal; "> <img class="imageNode" style="vertical-align: baseline;width: 294px;height: 89px" src="data:image/png;base64,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" data-image-state="image-loaded" width="294" height="89"></div><div style="block-size: 37.8px; 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 18.9px; text-align: left; transform-origin: 384px 18.9px; 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: 163px 7px; transform-origin: 163px 7px; unicode-bidi: normal; ">Since this problem involves unbelievable sums of money,<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: 116px 7px; transform-origin: 116px 7px; unicode-bidi: normal; "> please reduce your answer modulo <img src="data:image/png;base64,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" style="width: 50px; height: 16px;" width="50" height="16"><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: 71px 7px; transform-origin: 71px 7px; unicode-bidi: normal; ">. Therefore for the above example the final answer should be:</div><div style="background-color: rgb(247, 247, 247); block-size: 55.2px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 27.6px; transform-origin: 404px 27.6px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; "><div style="background-color: rgba(0, 0, 0, 0); block-size: 18.4px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; 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; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 9.2px; transform-origin: 404px 9.2px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 115.5px 7.5px; tab-size: 4; transform-origin: 115.5px 7.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "> &gt;&gt; k = mod([-30,20,80],2178309)</div><div style="background-color: rgba(0, 0, 0, 0); block-size: 18.4px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; 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; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 9.2px; transform-origin: 404px 9.2px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 28px 7.5px; tab-size: 4; transform-origin: 28px 7.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "> k =</div><div style="background-color: rgba(0, 0, 0, 0); block-size: 18.4px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; 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; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 9.2px; transform-origin: 404px 9.2px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 73.5px 7.5px; tab-size: 4; transform-origin: 73.5px 7.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "> 2178279 20 80</div></div><div style="block-size: 56.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 28.35px; text-align: left; transform-origin: 384px 28.35px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; 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: 15px 7px; transform-origin: 15px 7px; unicode-bidi: normal; ">HINT<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: 321.5px 7px; transform-origin: 321.5px 7px; unicode-bidi: normal; ">: Use of a big integer arithmetic implementation, is not required in this problem. You can get the modulus using <a target='_blank' href = "https://en.wikipedia.org/wiki/Pisano_period">Pisano Period</a><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: 4px 7px; transform-origin: 4px 7px; unicode-bidi: normal; ">. <img src="data:image/png;base64,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" style="width: 50px; height: 16px;" width="50" height="16"><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: 20px 7px; transform-origin: 20px 7px; unicode-bidi: normal; "> is the <img src="data:image/png;base64,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" style="width: 16px; height: 16px;" width="16" height="16"><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: 11px 7px; transform-origin: 11px 7px; unicode-bidi: normal; ">-nd <a target='_blank' href = "https://en.wikipedia.org/wiki/Fibonacci_number">Fibonacci number.</a><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: 213px 7px; transform-origin: 213px 7px; unicode-bidi: normal; "> Also, the ratio of the day's ending balance to the deposit approaches the <a target='_blank' href = "https://en.wikipedia.org/wiki/Golden_ratio">Golden Ratio</a><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: 11px 7px; transform-origin: 11px 7px; unicode-bidi: normal; "> as the values of n<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: 36px 7px; transform-origin: 36px 7px; unicode-bidi: normal; "> gets larger. </div></div></div>

In fantasy world where money does grow on trees, a man decided to top-up his bank account, daily. On the first day he noticed that he has initial "integer" balance of , so he made his first "integer" deposit of . On the next days, he made deposit equivalent to the day's starting balance plus the amount he deposited on the previous day. This means that on any -th day the following formula for the amount he would deposit, holds:  .
Given that on the -th day, he made a deposit of , calculate his initial balance  , his first deposit , and his final ending balance at the end of the -th day transaction. It is also known that the first deposit he made () is the smallest possible first deposit to attain  at the -th day, using the above formula.
While the account balances can be negative, deposits are always positive (no withdrawals please).
For example, bank statements if  and , are shown below. His first deposit , is the smallest possible first deposit to attain a deposit of  on the -th day. His starting balance should be , and his ending balance at -th day should be . 
                        
Since this problem involves unbelievable sums of money, please reduce your answer modulo . Therefore for the above example the final answer should be:
  >> k = mod([-30,20,80],2178309)
     k =
        2178279 20 80
HINT: Use of a big integer arithmetic implementation, is not required in this problem. You can get the modulus using Pisano Period.  is the -nd Fibonacci number. Also, the ratio of the day's ending balance to the deposit approaches the Golden Ratio as the values of  gets larger.

Solve

Solution Stats

2 Solutions
2 Solvers

Last Solution submitted on Dec 15, 2022

Last 200 Solutions

Problem Comments

1 Comment

1 Comment

GeeTwo on 15 Dec 2022

Noete that Test 12 not only forbids java, BigInteger, persistent, and global, but also control structures: if, for, switch, while, try.

Also, there's a song in there somewhere:

Fibonacci, number thirty two
♫ ♪ ♩ ♫ ♩ ♫ ♩ ♪ ♩
two one seven eight three oh ni-i-ine

Problem Recent Solvers2

Problem Tags

Community Treasure Hunt

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

Start Hunting!

Problem 56065. Easy Sequences 74: Fibonacci Bank Account

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers2

Suggested Problems

More from this Author101

Problem Tags

Community Treasure Hunt

Problem 56065. Easy Sequences 74: Fibonacci Bank Account

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers2

Suggested Problems

More from this Author101

Problem Tags

Community Treasure Hunt

Players