Algebra.Com's Answer #835286 by ikleyn(52786)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "Asset X generates a perpetual stream of cash flows of $100,000 every 3 months.
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document.write( "The relevant interest rate is 12%, compounded quarterly.
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document.write( "How much would you pay to buy Asset X today if the first payment occurs right away?
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document.write( " Probably, a professional finansist can solve this problem faster than me,\r
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document.write( " but I can explain the solution better for a non-professional reader.\r
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document.write( "The question is as follows:\r\n" );
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document.write( " If you have enough amount of money Y, what is better for you:\r\n" );
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document.write( " deposit this amount Y \"all in one time\" today into a bank at 12% compounded quarterly\r\n" );
document.write( " or to buy today an asset X for Y dollars, from which you will deposit \r\n" );
document.write( " $100,000 every 3 months to a bank at 12% compounded quarterly?\r\n" );
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document.write( "First option generates the amount of A =  =  = 1.125509*Y dollars in one year.\r\n" );
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document.write( "Second option works as an Annuity Due saving plan and generates the amout \r\n" );
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document.write( " B =  =  = $430913.58 (rounded) in one year.\r\n" );
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document.write( "Therefore, the reasonable value/price to buy the asset X for one year is no more than \r\n" );
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document.write( " Y =  = $382861.07 dollars.\r\n" );
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document.write( "Thus, we calculated the reasonable value/price to buy the asset X for one year.\r\n" );
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document.write( " Next, let's consider more longer time intervals of n = 3, 5, 10, 20, 50 and 100 years.\r\n" );
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document.write( "We should calculate A(n) and B(n) using the formulas\r\n" );
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document.write( " A(n) =  , B(n) =  \r\n" );
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document.write( "and the ratio Y(n) =  , which is the reasonable value/price to buy the asset X for n year.\r\n" );
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document.write( "The table for the values of n, B(n) and Y(n) is shown/computed below\r\n" );
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document.write( " n Y(n) B(n)\r\n" );
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document.write( " 1 430914 382861\r\n" );
document.write( " 3 1461779 1025262\r\n" );
document.write( " 5 2767649 1532380\r\n" );
document.write( " 10 7766330 2380822\r\n" );
document.write( " 20 3310039 3110679\r\n" );
document.write( " 50 1264688299 3424038\r\n" );
document.write( " 100 468384665935 3433308\r\n" );
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document.write( "From the table, it is seen that the values of B(n) raise significantly for n = 1, 3, 5, 10, 20 years, \r\n" );
document.write( "but after that, for n = 50, 100 years tends to some limit (to stabilization).\r\n" );
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document.write( "As everybody understands, the 12% percentage account is non-realistic for such long time as 20-30-50 years \r\n" );
document.write( "- - - therefore, I made my calculations in this lesson to present you more realistic picture.\r\n" );
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document.write( "Solved.\r
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document.write( "On Annuity Due saving plan, see my lesson\r
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document.write( " - Annuity Due saving plans and geometric progressions\r
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document.write( "in this site www.algebra.com.\r
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