<?xml version="1.0" encoding="us-ascii"?><InstanceReport xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xsd="http://www.w3.org/2001/XMLSchema"><Version>2.2.0.25</Version><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><ReportLongName>112 - Disclosure - Federal Funds Sold, Securities Purchased under Agreements to Resell and Other Short-Term Investment Securities</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelColumn>false</LabelColumn><CurrencyCode>USD</CurrencyCode><FootnoteIndexer /><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName>1/1/2011 - 3/31/2011
USD ($)

USD ($) / shares
</KeyName><CurrencySymbol>$</CurrencySymbol><contextRef><ContextID>eol_PE9839----1110-Q0003_STD_90_20110331_0</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0000719739</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2011-01-01T00:00:00</PeriodStartDate><PeriodEndDate>2011-03-31T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS><UnitProperty><UnitID>iso4217_USD</UnitID><UnitType>Standard</UnitType><StandardMeasure><MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema><MeasureValue>USD</MeasureValue><MeasureNamespace>iso4217</MeasureNamespace></StandardMeasure><Scale>0</Scale></UnitProperty><UnitProperty><UnitID>iso4217_USD_per_shares</UnitID><UnitType>Divide</UnitType><NumeratorMeasure><MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema><MeasureValue>USD</MeasureValue><MeasureNamespace>iso4217</MeasureNamespace></NumeratorMeasure><DenominatorMeasure><MeasureSchema>http://www.xbrl.org/2003/instance</MeasureSchema><MeasureValue>shares</MeasureValue><MeasureNamespace /></DenominatorMeasure><Scale>0</Scale></UnitProperty></UPS><CurrencyCode>USD</CurrencyCode><OriginalCurrencyCode>USD</OriginalCurrencyCode></MCU><CurrencySymbol>$</CurrencySymbol><Labels><Label Id="1" Label="3 Months Ended" /><Label Id="2" Label="Mar. 31, 2011" /></Labels></Column></Columns><Rows><Row><Id>5</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><Level>0</Level><ElementName>sivb_FederalFundsSoldSecuritiesPurchasedUnderAgreementToResellAndOtherShortTermInvestmentSecuritiesDisclosureTextBlock</ElementName><ElementPrefix>sivb</ElementPrefix><IsBaseElement>false</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><ShortDefinition>Disclosure of Federal Funds Sold, Securities Purchased under Agreements to Resell and Other Short-Term Investment Securities.</ShortDefinition><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsSubReportEnd>false</IsSubReportEnd><IsCalendarTitle>false</IsCalendarTitle><IsTuple>false</IsTuple><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole>verboselabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;div&gt;
&lt;p style="margin-top:18px;margin-bottom:0px"&gt;&lt;font style="font-family:Times New Roman" size="2"&gt;&lt;b&gt;4. Federal Funds Sold,
Securities Purchased under Agreements to Resell and Other
Short-Term Investment Securities&lt;/b&gt;&lt;/font&gt;&lt;/p&gt;
&lt;p style="margin-top:6px;margin-bottom:0px; text-indent:4%"&gt;
&lt;font style="font-family:Times New Roman" size="2"&gt;The following
table details the securities purchased under agreements to resell
and other short-term investment securities at March&amp;#xA0;31, 2011
and December&amp;#xA0;31, 2010, respectively:&lt;/font&gt;&lt;/p&gt;
&lt;p style="font-size:12px;margin-top:0px;margin-bottom:0px"&gt;
&amp;#xA0;&lt;/p&gt;
&lt;table cellspacing="0" cellpadding="0" width="100%" border="0" align="center"&gt;
&lt;tr&gt;
&lt;td width="76%"&gt;&lt;/td&gt;
&lt;td valign="bottom" width="6%"&gt;&lt;/td&gt;
&lt;td&gt;&lt;/td&gt;
&lt;td&gt;&lt;/td&gt;
&lt;td&gt;&lt;/td&gt;
&lt;td valign="bottom" width="6%"&gt;&lt;/td&gt;
&lt;td&gt;&lt;/td&gt;
&lt;td&gt;&lt;/td&gt;
&lt;td&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td valign="bottom" nowrap="nowrap" style="border-bottom:1px solid #000000"&gt;
&lt;p style="margin-top:0px;margin-bottom:1px"&gt;&lt;font style="font-family:Times New Roman" size="1"&gt;&lt;b&gt;(Dollars in
thousands)&lt;/b&gt;&lt;/font&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" colspan="2" align="center" style="border-bottom:1px solid #000000"&gt;&lt;font style="font-family:Times New Roman" size="1"&gt;&lt;b&gt;March&amp;#xA0;31,&amp;#xA0;2011&lt;/b&gt;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" colspan="2" align="center" style="border-bottom:1px solid #000000"&gt;&lt;font style="font-family:Times New Roman" size="1"&gt;&lt;b&gt;December&amp;#xA0;31,&amp;#xA0;2010&lt;/b&gt;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr bgcolor="#CCEEFF"&gt;
&lt;td valign="top"&gt;
&lt;p style="margin-left:1.00em; text-indent:-1.00em"&gt;&lt;font style="font-family:Times New Roman" size="2"&gt;Securities purchased under
agreements to resell&lt;/font&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font style="font-family:Times New Roman" size="2"&gt;$&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" align="right"&gt;&lt;font style="font-family:Times New Roman" size="2"&gt;19,687&lt;/font&gt;&lt;/td&gt;
&lt;td nowrap="nowrap" valign="bottom"&gt;&lt;font style="font-family:Times New Roman" size="2"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font style="font-family:Times New Roman" size="2"&gt;$&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" align="right"&gt;&lt;font style="font-family:Times New Roman" size="2"&gt;60,345&lt;/font&gt;&lt;/td&gt;
&lt;td nowrap="nowrap" valign="bottom"&gt;&lt;font style="font-family:Times New Roman" size="2"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td valign="top"&gt;
&lt;p style="margin-left:1.00em; text-indent:-1.00em"&gt;&lt;font style="font-family:Times New Roman" size="2"&gt;Short-term agency discount
notes&lt;/font&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font style="font-family:Times New Roman" size="2"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" align="right"&gt;&lt;font style="font-family:Times New Roman" size="2"&gt;234,215&lt;/font&gt;&lt;/td&gt;
&lt;td nowrap="nowrap" valign="bottom"&gt;&lt;font style="font-family:Times New Roman" size="2"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font style="font-family:Times New Roman" size="2"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" align="right"&gt;&lt;font style="font-family:Times New Roman" size="2"&gt;330,370&lt;/font&gt;&lt;/td&gt;
&lt;td nowrap="nowrap" valign="bottom"&gt;&lt;font style="font-family:Times New Roman" size="2"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr bgcolor="#CCEEFF"&gt;
&lt;td valign="top"&gt;
&lt;p style="margin-left:1.00em; text-indent:-1.00em"&gt;&lt;font style="font-family:Times New Roman" size="2"&gt;Other short-term investment
securities&lt;/font&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font style="font-family:Times New Roman" size="2"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" align="right"&gt;&lt;font style="font-family:Times New Roman" size="2"&gt;22,310&lt;/font&gt;&lt;/td&gt;
&lt;td nowrap="nowrap" valign="bottom"&gt;&lt;font style="font-family:Times New Roman" size="2"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font style="font-family:Times New Roman" size="2"&gt;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" align="right"&gt;&lt;font style="font-family:Times New Roman" size="2"&gt;12,992&lt;/font&gt;&lt;/td&gt;
&lt;td nowrap="nowrap" valign="bottom"&gt;&lt;font style="font-family:Times New Roman" size="2"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr style="font-size:1px"&gt;
&lt;td valign="bottom"&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&amp;#xA0;&amp;#xA0;&lt;/td&gt;
&lt;td valign="bottom" style="border-top:1px solid #000000"&gt;
&amp;#xA0;&lt;/td&gt;
&lt;td valign="bottom" style="border-top:1px solid #000000"&gt;
&amp;#xA0;&lt;/td&gt;
&lt;td&gt;&amp;#xA0;&lt;/td&gt;
&lt;td valign="bottom"&gt;&amp;#xA0;&amp;#xA0;&lt;/td&gt;
&lt;td valign="bottom" style="border-top:1px solid #000000"&gt;
&amp;#xA0;&lt;/td&gt;
&lt;td valign="bottom" style="border-top:1px solid #000000"&gt;
&amp;#xA0;&lt;/td&gt;
&lt;td&gt;&amp;#xA0;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td valign="top"&gt;
&lt;p style="margin-left:1.00em; text-indent:-1.00em"&gt;&lt;font style="font-family:Times New Roman" size="2"&gt;Total federal funds sold,
securities purchased under agreements to resell and other
short-term investment securities&lt;/font&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font style="font-family:Times New Roman" size="2"&gt;$&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" align="right"&gt;&lt;font style="font-family:Times New Roman" size="2"&gt;276,212&lt;/font&gt;&lt;/td&gt;
&lt;td nowrap="nowrap" valign="bottom"&gt;&lt;font style="font-family:Times New Roman" size="2"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font size="1"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&lt;font style="font-family:Times New Roman" size="2"&gt;$&lt;/font&gt;&lt;/td&gt;
&lt;td valign="bottom" align="right"&gt;&lt;font style="font-family:Times New Roman" size="2"&gt;403,707&lt;/font&gt;&lt;/td&gt;
&lt;td nowrap="nowrap" valign="bottom"&gt;&lt;font style="font-family:Times New Roman" size="2"&gt;&amp;#xA0;&amp;#xA0;&lt;/font&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr style="font-size:1px"&gt;
&lt;td valign="bottom"&gt;&lt;/td&gt;
&lt;td valign="bottom"&gt;&amp;#xA0;&amp;#xA0;&lt;/td&gt;
&lt;td valign="bottom" style="border-top:3px double #000000"&gt;
&amp;#xA0;&lt;/td&gt;
&lt;td valign="bottom" style="border-top:3px double #000000"&gt;
&amp;#xA0;&lt;/td&gt;
&lt;td&gt;&amp;#xA0;&lt;/td&gt;
&lt;td valign="bottom"&gt;&amp;#xA0;&amp;#xA0;&lt;/td&gt;
&lt;td valign="bottom" style="border-top:3px double #000000"&gt;
&amp;#xA0;&lt;/td&gt;
&lt;td valign="bottom" style="border-top:3px double #000000"&gt;
&amp;#xA0;&lt;/td&gt;
&lt;td&gt;&amp;#xA0;&lt;/td&gt;
&lt;/tr&gt;
&lt;/table&gt;
&lt;p style="margin-top:12px;margin-bottom:0px; text-indent:4%"&gt;
&lt;font style="font-family:Times New Roman" size="2"&gt;In addition, as
of March&amp;#xA0;31, 2011 and December&amp;#xA0;31, 2010, $1.5 billion and
$2.2 billion, respectively, of our cash and due from banks was
deposited with the Federal Reserve Bank and was earning interest at
the Federal Funds target rate, and interest-earning deposits in
other financial institutions were $265.3 million and $246.3
million, respectively.&lt;/font&gt;&lt;/p&gt;
&lt;/div&gt;</NonNumbericText><NonNumericTextHeader>4. Federal Funds Sold,
Securities Purchased under Agreements to Resell and Other
Short-Term Investment Securities

The following
table details the securities</NonNumericTextHeader><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios></Cell></Cells><OriginalInstanceReportColumns /><Unit>Other</Unit><ElementDataType>us-types:textBlockItemType</ElementDataType><SimpleDataType>string</SimpleDataType><ElementDefenition>Disclosure of Federal Funds Sold, Securities Purchased under Agreements to Resell and Other Short-Term Investment Securities.</ElementDefenition><ElementReferences>No authoritative reference available.</ElementReferences><IsTotalLabel>false</IsTotalLabel><IsEPS>false</IsEPS><Label>Federal Funds Sold, Securities Purchased under Agreements to Resell and Other Short-Term Investment Securities</Label></Row></Rows><Footnotes /><NumberOfCols>1</NumberOfCols><NumberOfRows>1</NumberOfRows><ReportName>Federal Funds Sold, Securities Purchased under Agreements to Resell and Other Short-Term Investment Securities</ReportName><MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel><SharesRoundingLevel>UnKnown</SharesRoundingLevel><PerShareRoundingLevel>UnKnown</PerShareRoundingLevel><ExchangeRateRoundingLevel>UnKnown</ExchangeRateRoundingLevel><HasCustomUnits>false</HasCustomUnits><SharesShouldBeRounded>true</SharesShouldBeRounded></InstanceReport>
