document.write( "Question 1186537: A bank earns 3% interest per annum compounded monthly for an initial savings deposit of 100,000 pesos. Find the net value of the deposit after 3 quarters if the earning is subjected to a 21% tax.
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Algebra.Com's Answer #849476 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "A bank earns 3% interest per annum compounded monthly for an initial savings deposit of 100,000 pesos.
\n" ); document.write( "Find the net value of the deposit after 3 quarters if the earning is subjected to a 21% tax.
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\n" ); document.write( "\n" ); document.write( "        In the post by @CPhill, the chart flow (the sequence) of calculations is correct,\r
\n" ); document.write( "\n" ); document.write( "        but the precision is not enough, so his resulting value (his answer) is not absolutely correct.\r
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\n" ); document.write( "\n" ); document.write( "        I will repeat here all his steps, using Excel as my calculator, \r
\n" ); document.write( "\n" ); document.write( "        and will get another answer with quite visible/significant difference.\r
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document.write( "1. **Calculate the interest rate per month:**\r\n" );
document.write( "   The annual interest rate is 3%, so the monthly interest rate is 3% / 12 = 0.25% or 0.0025 as a decimal.\r\n" );
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document.write( "2. **Calculate the number of months in 3 quarters:**\r\n" );
document.write( "   There are 3 months in a quarter, so 3 quarters is equal to 3 * 3 = 9 months.\r\n" );
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document.write( "3. **Calculate the future value of the deposit before tax:**\r\n" );
document.write( "   We use the formula for compound interest:\r\n" );
document.write( "   Future Value = Principal * (1 + interest rate)^number of periods\r\n" );
document.write( "   Future Value = 100,000 * (1 + 0.0025)^9\r\n" );
document.write( "   Future Value = 100,000 * (1.0025)^9\r\n" );
document.write( "   Future Value ≈ 100,000 * 1.022726317  <<<---===  it is first place, where my number is different from @CPhill.\r\n" );
document.write( "   Future Value ≈ 102,272.63 pesos       <<<---===  @CPhill gives here 102,260 pesos. \r\n" );
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document.write( "4. **Calculate the tax amount:**\r\n" );
document.write( "   The tax rate is 21%, so the tax amount is:\r\n" );
document.write( "   Tax = Future Value * tax rate\r\n" );
document.write( "   Tax = 102,272.63 * 0.21\r\n" );
document.write( "   Tax ≈ 21,477.25 pesos\r\n" );
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document.write( "5. **Calculate the net value after tax:**\r\n" );
document.write( "   Net Value = Future Value - Tax\r\n" );
document.write( "   Net Value = 102,272.63 - 21,477.25\r\n" );
document.write( "   Net Value ≈ 80,795.38 pesos\r\n" );
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document.write( "Therefore, the net value of the deposit after 3 quarters, after the 21% tax is applied, is 80,795.38 pesos.\r\n" );
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document.write( "Compare here with the answer by 80,785.40 by @CPhill.\r\n" );
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document.write( "The difference appeared, because @CPhill in his calculations makes intermediate rounding, losing precision.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved correctly, to get perfectly correct answer.\r
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\n" ); document.write( "\n" ); document.write( "The rule of such calculations is: do not make intermediate rounding.\r
\n" ); document.write( "\n" ); document.write( " Make the final rounding at the end, ONLY.\r
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\n" ); document.write( "\n" ); document.write( "At this forum, I just noticed and pointed out a similar error/deficiency in the post by @CPhill under the link\r
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\n" ); document.write( "\n" ); document.write( "\n" ); document.write( ">https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1190651.html
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\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1190651.html\r
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