document.write( "Question 1203727: On average, it needs Php 250,000 per year and an additional Php 600,000 every 4 years for major repairs to maintain a certain three-storey office building. How much must be paid now to take care of these payments on a bank that offers 8% per year? \n" ); document.write( "

Algebra.Com's Answer #839525 by ikleyn(52851) $\"\"$ $\"About$

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\n" ); document.write( "On average, it needs Php 250,000 per year and an additional Php 600,000 every 4 years for major repairs
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\n" ); document.write( "of these payments on a bank that offers 8% per year?
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document.write( "We follow to this scheme/scenario.\r\n" );
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document.write( "(0)  At the end of the year \"0\", person A deposits the amount of Php X to the bank.   \r\n" );
document.write( "     The value of X is unknown and should be determine in the solution.\r\n" );
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document.write( "(1)  On Jan 1 of the year 1, the person withdraws Php 250,000 for the regular annual repair.\r\n" );
document.write( "     Now, there are (X-250000) Php at the account.\r\n" );
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document.write( "     On Dec 1 of the year 1, these (X-250000) Php become (X-250000)*1.08 Php after compounding.\r\n" );
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document.write( "(2)  On Jan 1 of the year 2, the person withdraws Php 250,000 for the regular annual repair.\r\n" );
document.write( "     Now, there are (X-250000)*1.08-250000 Php at the account.\r\n" );
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document.write( "     On Dec 1 of the year 2, these (X-250000)*1.08-250000  Php become ((X-250000)*1.08-250000)*1.08 Php after compounding.\r\n" );
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document.write( "(3)  On Jan 1 of the year 3, the person withdraws Php 250,000 for the regular annual repair.\r\n" );
document.write( "     Now, there are ((X-250000)*1.08-250000)*1.08-250000  Php at the account.\r\n" );
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document.write( "     On Dec 1 of the year 2, these ((X-250000)*1.08-250000)*1.08-250000 Php become (((X-250000)*1.08-250000)*1.08-250000)*1.08 Php after compounding.\r\n" );
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document.write( "(4)  On Jan 1 of the year 4, the person withdraw Php 250,000 for the regular annual repair, and he (or she) should still have\r\n" );
document.write( "     enough remaining money at the account to cover Php 600,000 of the 4-years repair.\r\n" );
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document.write( "So, this equation should be held\r\n" );
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document.write( "     (((X-250000)*1.08-250000)*1.08-250000)*1.08 - 250000 = 600000.\r\n" );
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document.write( "From this equation, we should find the unknown value of X.\r\n" );
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document.write( "To do it, simplify this equation, step by step.\r\n" );
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document.write( "     (((X-250000)*1.08-250000)*1.08-250000)*1.08 = 600000 + 250000\r\n" );
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document.write( "     (((X-250000)*1.08-250000)*1.08-250000)*1.08 = 850000\r\n" );
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document.write( "Divide both sides by 1.08\r\n" );
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document.write( "     ((X-250000)*1.08-250000)*1.08-250000 = 850000/1.08 \r\n" );
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document.write( "     ((X-250000)*1.08-250000)*1.08-250000 = 787037.04      (I am rounding to the closest cent)\r\n" );
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document.write( "     ((X-250000)*1.08-250000)*1.08 = 250000 + 787037.04   \r\n" );
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document.write( "     ((X-250000)*1.08-250000)*1.08 = 1037037.04   \r\n" );
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document.write( "Divide both sides by 1.08\r\n" );
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document.write( "     (X-250000)*1.08-250000 = 1037037.04/1.08   \r\n" );
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document.write( "     (X-250000)*1.08-250000 = 960219.48                    (I am rounding to the closest cent)\r\n" );
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document.write( "     (X-250000)*1.08 = 250000 + 960219.48   \r\n" );
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document.write( "     (X-250000)*1.08 = 1210219.48\r\n" );
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document.write( "Divide both sides by 1.08\r\n" );
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document.write( "      X-250000 = 1210219.48/1.08\r\n" );
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document.write( "      X-250000 = 1120573.59                                (I am rounding to the closest cent)\r\n" );
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document.write( "         X     = 250000 + 1120573.59\r\n" );
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document.write( "         X     = 1370573.59\r\n" );
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document.write( "ANSWER.  The original / (initial) deposit should be  Php 1,370,573.59.\r\n" );
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document.write( "Compare it with the required amount of Php 600,000 + Php 4*250,000 = Php 1,600,000 if the compounded account is not used.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, with complete and clear explanation.\r
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\n" ); document.write( "\n" ); document.write( "It can be solved using more complicated technique, but in this post
\n" ); document.write( "my goal was to explain the idea clearly, not the advanced technique.\r
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