document.write( "Question 1186451: What is the future value (as of 10 years from now) of an annuity that makes 10 annual payments of P 5,000, if the interest rate is 7% per year compounded quarterly? \n" ); document.write( "

Algebra.Com's Answer #849384 by ikleyn(52802) $\"\"$ $\"About$

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\n" ); document.write( "What is the future value (as of 10 years from now) of an annuity that makes 10 annual payments
\n" ); document.write( "of P5,000, if the interest rate is 7% per year compounded quarterly?
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\n" ); document.write( "\n" ); document.write( "        My understanding is that they want to find future value of the ordinary annuity saving plan\r
\n" ); document.write( "\n" ); document.write( "        in 10 years from now, given that a person makes 10 deposits of P5000 each at the end of each \r
\n" ); document.write( "\n" ); document.write( "        of 10 years. The interest rate in the bank is 7% per year compounded quarterly.\r
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document.write( "The complication is that the deposits are made annually, while compounding are made quarterly.\r\n" );
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document.write( "So, we should construct an equivalent model, which will smoothly combine/treat these features.\r\n" );
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document.write( "7% annually compounded quarterly works as the effective quarterly rate r = 0.07/4;\r\n" );
document.write( "then the effective annual growth coefficient is\r\n" );
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document.write( "    t =  = 1.071859031,  or an effective annual rate q = 0.071859031.\r\n" );
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document.write( "Now this given saving plan as an equivalent to the ordinary annuity \r\n" );
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document.write( "with annual deposits of P5000 and with effective annual rate q = 0.071859031 compounding yearly.\r\n" );
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document.write( "Therefore, we can apply the standard formula for future value of such ordinary annuity\r\n" );
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document.write( "    FV =  = 69691.82.\r\n" );
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document.write( "ANSWER.  The future value is P69691.82.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved completely, with complete explanations.\r
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\n" ); document.write( "\n" ); document.write( "We equivalently transformed the given saving plan into another saving plan,
\n" ); document.write( "where deposits are synchronized with compounding.\r
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