document.write( "Question 1153297: how long will it take to save $20,000 by making deposits of $100 at the end of every month into an account earning interest at 6% compounded quarterly? \n" ); document.write( "

Algebra.Com's Answer #775486 by ikleyn(52847) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "It works by the same way, as if the account is compounded quarterly.\r
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document.write( "It is a classic Ordinary Annuity saving plan. The general formula is \r\n" );
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document.write( "    FV = ,    (1)\r\n" );
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document.write( "where  FV is the future value of the account;  P is the quarterly deposit; r is the quarterly percentage yield presented as a decimal; \r\n" );
document.write( "n is the number of deposits (= the number of quarters, in this case).\r\n" );
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document.write( "Under the given conditions, P = 100;  r = 0.06/4.  So, according to the formula (1), you get at the end of the n-th quarter\r\n" );
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document.write( "    FV =  = .\r\n" );
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document.write( "You want to find n from the inequality\r\n" );
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document.write( "     >= 20000.\r\n" );
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document.write( "Then\r\n" );
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document.write( "     >=  = 3\r\n" );
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document.write( "     >= 4\r\n" );
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document.write( "    n*log(1.015) >= log(4)\r\n" );
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document.write( "    n >=  = 93.11\r\n" );
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document.write( "The preliminary ANSWER is  94 quarters, or  23 years and 2 quarters.\r\n" );
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document.write( "Let's check it. After 93 quarters, the amount will be\r\n" );
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document.write( "    FV =  = 19955.95.\r\n" );
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document.write( "So, actually  93 quarters and 1 month is enough to get $20000.\r\n" );
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document.write( "The final answer.  93 quarters and 1 month, or  23 years and 4 months.\r\n" );
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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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