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Question

<div class="txt-body question-body"><div class="feedback-rating abuse-flag" data-questionid="12225437"></div><div class="ugc-base"><p>You have your choice of two investment accounts. Investment A isa 14-year annuity that features end-of-month $1,850 payments andhas an interest rate of 8.2 percent compounded monthly. InvestmentB is a 7.7 percent continuously compounded lump sum investment,also good for 14 years.</p><p>How much money would you need to invest in B today for it to beworth as much as Investment A 14 years from now? Amount needed:$__________</p></div></div>

Explanation / Answer

&lt;div class=&quot;txt-body answer-body&quot;&gt; &lt;div class=&quot;answer-given-body ugc-base&quot;&gt; &lt;p&gt;Solution:&lt;/p&gt;&lt;p&gt;To compute the amount earned from investment A and hence toarrive at the future value of the investment after 14 years we needto multiply with the future value interest annuity factor&lt;/p&gt;&lt;p&gt;= Future value annuity 14 years , 8.2% compounded monthly hencewe can convert to yearly therefore years = 14*12 = 168 and percentwould be = 8.2%/12 = .6833%&lt;/p&gt;&lt;p&gt;The value at the end of period from investment A would be = 1850* FVIFA (168 years , .6833%)&lt;/p&gt;&lt;p&gt;= 1850 *3.1340&lt;/p&gt;&lt;p&gt;= 5808.22 will be the value in 14 years of investment A&lt;/p&gt;&lt;p&gt;To compute the amount to be invested in investment B wouldbe&lt;/p&gt;&lt;p&gt;5808.22 = amount invested * present value 14 years 7.7percent&lt;/p&gt;&lt;p&gt;Amount invested = 5808.22/2.9283&lt;/p&gt;&lt;p&gt;&lt;strong&gt;= $1983.43&lt;/strong&gt;&lt;/p&gt; &lt;/div&gt; &lt;/div&gt;

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