document.write( "Question 1179711: Determine the periodic payments on the given loan or mortgage.
\n" ); document.write( "$5,000,000 borrowed at 7% for 30 years, with quarterly payments
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Algebra.Com's Answer #850186 by ikleyn(52920) $\"\"$ $\"About$

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\n" ); document.write( "Determine the periodic payments on the given loan or mortgage.
\n" ); document.write( "$5,000,000 borrowed at 7% for 30 years, with quarterly payments
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\n" ); document.write( "\n" ); document.write( "        I used the same formulas as in the post by @CPhill.
\n" ); document.write( "        I calculated using MS Excel and Google spreadsheets.
\n" ); document.write( "        My final result is different from that by @CPhill.\r
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document.write( "Here's how to calculate the quarterly payment for the loan:\r\n" );
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document.write( "**1. Given Information:**\r\n" );
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document.write( "* Principal (P): $5,000,000\r\n" );
document.write( "* Annual interest rate (r): 7% or 0.07\r\n" );
document.write( "* Loan term (t): 30 years\r\n" );
document.write( "* Compounding periods per year (n): 4 (quarterly)\r\n" );
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document.write( "**2. Calculate the Quarterly Interest Rate (i):**\r\n" );
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document.write( "* i = r / n = 0.07 / 4 = 0.0175\r\n" );
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document.write( "**3. Calculate the Total Number of Payments (N):**\r\n" );
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document.write( "* N = n * t = 4 * 30 = 120\r\n" );
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document.write( "**4. Use the Loan Payment Formula:**\r\n" );
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document.write( "PMT = P * (i * (1 + i)^N) / ((1 + i)^N - 1)\r\n" );
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document.write( "Where:\r\n" );
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document.write( "* PMT = periodic payment\r\n" );
document.write( "* P = principal\r\n" );
document.write( "* i = interest rate per period\r\n" );
document.write( "* N = total number of payments\r\n" );
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document.write( "**5. Plug in the Values:**\r\n" );
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document.write( "PMT = 5000000 * (0.0175 * (1 + 0.0175)^120) / ((1 + 0.0175)^120 - 1)\r\n" );
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document.write( "PMT = 5000000 * (0.0175 * (1.0175)^120) / ((1.0175)^120 - 1)\r\n" );
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document.write( "PMT = 99965.84.     <<<---===  obtained from MS Excel and confirmed by Google spreadsheet.\r\n" );
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document.write( "**Answer:**\r\n" );
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document.write( "The quarterly payment (PMT) is $99,965.84.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "My answer is different from that by @CPhill.\r
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