document.write( "Question 1194023: Emmerson invests N$100,000.00 on a monthly basis, at the end of each month at an interest rate of 8.5% compounded quarterly.
\n" ); document.write( "a) How much will he have after 3.5 years?
\n" ); document.write( "b) How much interest does he earn on a monthly basis? (Hint: Calculate the monthly average. \n" ); document.write( "
Algebra.Com's Answer #826156 by ikleyn(52788)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "            I have different view on how this account works;\r
\n" ); document.write( "\n" ); document.write( "            therefore, my solution for question  (a)  is different from that by @Theo.\r
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\n" ); document.write( "\n" ); document.write( "            In my post below,  I am placing my solution for question  (a),  ONLY.\r
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\n" ); document.write( "\n" ); document.write( "            Question  (b)  is posed in unclear way,  so I will not answer it,  at all.\r
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document.write( "As I understand, this account works as follows:\r\n" );
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document.write( "    Emmerson invests 100,000 every month; but the bank makes compounding only once in 3 months.\r\n" );
document.write( "    So, every month investments of 100,000 wait to the end of the quarter, and only after that \r\n" );
document.write( "    the compounding is made and 300000 is added.\r\n" );
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document.write( "    So, it works as an usual Ordinary Annuity quarterly compound account with 300,000 quarterly deposits.\r\n" );
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document.write( "The standard general formula for Ordinary Annuity is \r\n" );
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document.write( "    FV = \"P%2A%28%28%281%2Br%29%5En-1%29%2Fr%29\",    (1)\r\n" );
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document.write( "where  FV is the future value of the account;  P is the quarterly payment (deposit); \r\n" );
document.write( "1+r is the quarterly growth factor; \r\n" );
document.write( "n is the number of deposits (= the number of years multiplied by 3.5, in this case).\r\n" );
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document.write( "Under the given conditions, P = 300,000;  r = 0.085/4;  n = 4*3.5 = 14.  \r\n" );
document.write( "So, according to the formula (1), Emmerson will get at the end of the 14 months\r\n" );
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document.write( "    FV = \"300000%2A%28%28%281%2B0.085%2F4%29%5E14-1%29%2F%28%280.085%2F4%29%29%29\" =  $4832444 dollars.\r\n" );
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document.write( "Note that Emmerson deposits only  3*100000*4*3.5 = 4200000 dollars in 3.5 years.  \r\n" );
document.write( "The rest  4832444 - 4200000 = 632444  is the interest which the account earns/accumulates in 3.5 years.\r\n" );
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\n" ); document.write( "\n" ); document.write( "So, the major difference between my solution and that by @Theo is that in my solution
\n" ); document.write( "monthly current deposits wait for the end of the quarter to be compounded, while @Theo
\n" ); document.write( "compounds them on the monthly basis, although it is not quite equivalent, and the bank does not work this way.\r
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\n" ); document.write( "\n" ); document.write( "The difference of $4866514 - $4832444 = $34,070 is the consequence of this inequivalence.\r
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\n" ); document.write( "\n" ); document.write( "On Ordinary Annuity saving plans,  see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Ordinary Annuity saving plans and geometric progressions\r
\n" ); document.write( "\n" ); document.write( "    - Solved problems on Ordinary Annuity saving plans\r
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\n" ); document.write( "\n" ); document.write( "The lessons contain  EVERYTHING  you need to know about this subject,  in clear and compact form.\r
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\n" ); document.write( "\n" ); document.write( "When you learn from these lessons,  you will be able to do similar calculations in semi-automatic mode.\r
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