document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202558>Question 1202558</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ron borrowed $1800 to finance a computer at 15.6%/a compounded monthly for 1 1/2 years.<BR>\n" );
document.write( "a) How much will his monthly payments be?<BR>\n" );
document.write( "b) How much more would Ron have to pay per month to pay the loan off 6 months early?<BR>\n" );
document.write( "c) How much interest would Ron save if he paid the loan off early?\r<BR>\n" );
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document.write( "<font color=red>Answers</font><BR>\n" );
document.write( "(a)  $112.80 per month<BR>\n" );
document.write( "(b)  $50.18 more<BR>\n" );
document.write( "(c)  He saves $74.64\r<BR>\n" );
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document.write( "Work Shown for part (a)\r<BR>\n" );
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document.write( "The formula to use is<BR>\n" );
document.write( "P = (L*i)/( 1-(1+i)^(-n) )<BR>\n" );
document.write( "where,<BR>\n" );
document.write( "P = monthly payment<BR>\n" );
document.write( "L = loan amount<BR>\n" );
document.write( "i = monthly interest rate in decimal form<BR>\n" );
document.write( "n = number of months\r<BR>\n" );
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document.write( "In this case<BR>\n" );
document.write( "L = 1800<BR>\n" );
document.write( "i = 0.156/12 = 0.013 exactly<BR>\n" );
document.write( "n = 1.5*12 = 18 months\r<BR>\n" );
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document.write( "We can now compute the monthly payment.<BR>\n" );
document.write( "P = (L*i)/( 1-(1+i)^(-n) )<BR>\n" );
document.write( "P = (1800*0.013)/( 1-(1+0.013)^(-18) )<BR>\n" );
document.write( "P = 112.801552357259<BR>\n" );
document.write( "P = 112.80\r<BR>\n" );
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document.write( "Ron's monthly payment is $112.80<BR>\n" );
document.write( "It can be verified through use of a calculator such as this<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://www.calculator.net/loan-calculator.html\">https://www.calculator.net/loan-calculator.html</a>\r<BR>\n" );
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document.write( "Work Shown for part (b)\r<BR>\n" );
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document.write( "If he is required to pay back the loan 6 months early, then the 18 month time frame shrinks to 18-6 = 12 months.\r<BR>\n" );
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document.write( "We'll use n = 12 this time but keep the other values the same.\r<BR>\n" );
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document.write( "P = (L*i)/( 1-(1+i)^(-n) )<BR>\n" );
document.write( "P = (1800*0.013)/( 1-(1+0.013)^(-12) )<BR>\n" );
document.write( "P = 162.975019846114<BR>\n" );
document.write( "P = 162.98\r<BR>\n" );
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document.write( "Ron's monthly payment is now $162.98\r<BR>\n" );
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document.write( "Subtract the previous monthly payment to find the increase.<BR>\n" );
document.write( "162.98 - 112.80 = 50.18\r<BR>\n" );
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document.write( "He must pay $50.18 more per month if he wants to pay the loan back 6 months early.\r<BR>\n" );
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document.write( "Work Shown for part (c)\r<BR>\n" );
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document.write( "In part (a) we found Ron's monthly payment was $112.80<BR>\n" );
document.write( "Over the course of 18 months, he pays back a total of 18*112.80 = 2030.40 dollars.<BR>\n" );
document.write( "The interest is 2030.40 - 1800 = 230.40 dollars.\r<BR>\n" );
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document.write( "In part (b) we found Ron's monthly payment was $162.98<BR>\n" );
document.write( "Over the course of 12 months, he pays back a total of 12*162.98 = 1955.76 dollars.<BR>\n" );
document.write( "The interest is 1955.76 - 1800 = 155.76 dollars.\r<BR>\n" );
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document.write( "As you can see, Ron paying more per month has the advantage of paying less overall interest.\r<BR>\n" );
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document.write( "Subtract the interest amounts to determine how much he saves.<BR>\n" );
document.write( "230.40 - 155.76 = 74.64\r<BR>\n" );
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document.write( "He would save $74.64 if he pays back the loan 6 months early.<BR>\n" );
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