document.write( "Question 1198080: Find the periodic payments PMT necessary to accumulate the given amount in an annuity account. (Assume end-of-period deposits and compounding at the same intervals as deposits. Round your answer to the nearest cent.)\r
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Algebra.Com's Answer #852122 by ikleyn(52778) $\"\"$ $\"About$

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\n" ); document.write( "The periodic payments PMT necessary to accumulate the given amount in an annuity account.
\n" ); document.write( "(Assume end-of-period deposits and compounding at the same intervals as deposits).
\n" ); document.write( "$50,000 in a fund paying 5% per year, with monthly payments for 5 years, if the fund contains $10,000 at the start.
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document.write( "Let solve the problem in 2 steps.\r\n" );
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document.write( "                           Step 1\r\n" );
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document.write( "The future value of the initial amount of $10,000 in 5 years will be\r\n" );
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document.write( "     =  = 12,833.59 dollars.\r\n" );
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document.write( "Thus, making monthly deposits of X dollars, we should accrue  the rest  50000 - 12833.59 = 37166.41 dollars in 5 years,\r\n" );
document.write( "with compounding.\r\n" );
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document.write( "                           Step 2\r\n" );
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document.write( "Now we write the future value equation for an ordinary annuity with the monthly deposits of X dollars,\r\n" );
document.write( "compounded monthly at 5% annual interest\r\n" );
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document.write( "     = 37166.41,\r\n" );
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document.write( "We calculate the factor/multiplier at X separately, and we get this equation\r\n" );
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document.write( "    X*68.00608284 = 37166.41.\r\n" );
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document.write( "Solve for X and get the ANSWER\r\n" );
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document.write( "    X =  = 546.52.\r\n" );
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document.write( "At this point, the problem is solved completely.\r\n" );
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document.write( "The necessary monthly deposit is  546.52 dollars.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Hip-hip, hurray !\r
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