document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190544>Question 1190544</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Using the Loan Formula P_0= D(1-(1+r/k)^-Nk)` dividing by `(R/k)\r<BR>\n" );
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document.write( "Kyle is considering putting a 1000 laptop purchase on their credit card, which has an interest rate of 24% compounded monthly, how long will it take them to pay off the purchase if they make payments of 30 a month?\r<BR>\n" );
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document.write( "I am just stuck on the second step, if anyone can help thanks!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #822235 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3835)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=822235\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "N = number of months remaining  <BR>\n" );
document.write( "P = loan balance when N months remain<BR>\n" );
document.write( "D = 30 = monthly payment<BR>\n" );
document.write( "r = 0.24 = decimal form of the 24% interest rate<BR>\n" );
document.write( "k = 12 = number of payments per year (aka monthly)\r<BR>\n" );
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document.write( "r/k = 0.24/12 = 0.02\r<BR>\n" );
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document.write( "If we plugged in P = 1000 and solved for N, we would find the month number when the balance is $1000<BR>\n" );
document.write( "In other words, it would tell us how long the loan is.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+D%281-%281%2Br%2Fk%29%5E%28-N%29%29%2F%28r%2Fk%29 ALIGN=MIDDLE  ALT=\"P+=+D%281-%281%2Br%2Fk%29%5E%28-N%29%29%2F%28r%2Fk%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000+=+30%281-%281%2B0.02%29%5E%28-N%29%29%2F%280.02%29 ALIGN=MIDDLE  ALT=\"1000+=+30%281-%281%2B0.02%29%5E%28-N%29%29%2F%280.02%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000%2A0.02+=+30%281-%281.02%29%5E%28-N%29%29 ALIGN=MIDDLE  ALT=\"1000%2A0.02+=+30%281-%281.02%29%5E%28-N%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20+=+30%281-%281.02%29%5E%28-N%29%29 ALIGN=MIDDLE  ALT=\"20+=+30%281-%281.02%29%5E%28-N%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2F30+=+1-%281.02%29%5E%28-N%29 ALIGN=MIDDLE  ALT=\"20%2F30+=+1-%281.02%29%5E%28-N%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3+=+1-%281.02%29%5E%28-N%29 ALIGN=MIDDLE  ALT=\"2%2F3+=+1-%281.02%29%5E%28-N%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-%281.02%29%5E%28-N%29+=+2%2F3 ALIGN=MIDDLE  ALT=\"1-%281.02%29%5E%28-N%29+=+2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%281.02%29%5E%28-N%29+=+2%2F3-1 ALIGN=MIDDLE  ALT=\"-%281.02%29%5E%28-N%29+=+2%2F3-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%281.02%29%5E%28-N%29+=+-1%2F3 ALIGN=MIDDLE  ALT=\"-%281.02%29%5E%28-N%29+=+-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281.02%29%5E%28-N%29+=+1%2F3 ALIGN=MIDDLE  ALT=\"%281.02%29%5E%28-N%29+=+1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28%281.02%29%5E%28-N%29%29%29+=+log%28%281%2F3%29%29 ALIGN=MIDDLE  ALT=\"log%28%28%281.02%29%5E%28-N%29%29%29+=+log%28%281%2F3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-N%2Alog%28%281.02%29%29+=+log%28%281%2F3%29%29 ALIGN=MIDDLE  ALT=\"-N%2Alog%28%281.02%29%29+=+log%28%281%2F3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N+=+-log%28%281%2F3%29%29%2Flog%28%281.02%29%29 ALIGN=MIDDLE  ALT=\"N+=+-log%28%281%2F3%29%29%2Flog%28%281.02%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N+=+55.4781076387803 ALIGN=MIDDLE  ALT=\"N+=+55.4781076387803\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "That rounds up N = 56\r<BR>\n" );
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document.write( "Note what happens when N = 55<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+D%281-%281%2Br%2Fk%29%5E%28-N%29%29%2F%28r%2Fk%29 ALIGN=MIDDLE  ALT=\"P+=+D%281-%281%2Br%2Fk%29%5E%28-N%29%29%2F%28r%2Fk%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+30%281-%281%2B0.02%29%5E%28-55%29%29%2F%280.02%29 ALIGN=MIDDLE  ALT=\"P+=+30%281-%281%2B0.02%29%5E%28-55%29%29%2F%280.02%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+995.24362567013 ALIGN=MIDDLE  ALT=\"P+=+995.24362567013\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which is a bit short of $1,000\r<BR>\n" );
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document.write( "If we tried N = 56, then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+D%281-%281%2Br%2Fk%29%5E%28-N%29%29%2F%28r%2Fk%29 ALIGN=MIDDLE  ALT=\"P+=+D%281-%281%2Br%2Fk%29%5E%28-N%29%29%2F%28r%2Fk%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+30%281-%281%2B0.02%29%5E%28-56%29%29%2F%280.02%29 ALIGN=MIDDLE  ALT=\"P+=+30%281-%281%2B0.02%29%5E%28-56%29%29%2F%280.02%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+1005.14080948052 ALIGN=MIDDLE  ALT=\"P+=+1005.14080948052\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which is a bit over the target. So this confirms that N is somewhere between 55 and 56<BR>\n" );
document.write( "We round N up to the nearest whole number so that we guarantee to make the final monthly payment.\r<BR>\n" );
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document.write( "This is a handy calculator to check your work.<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.calculator.net/credit-card-calculator.html\">https://www.calculator.net/credit-card-calculator.html</a><BR>\n" );
document.write( "Type $1000 for the balance, 24% for the rate, and $30 for the min payment. Click the \"minimum payment\" radio button and click \"calculate\".<BR>\n" );
document.write( "The calculator should say \"It will take 4 years and 8 months to payoff the balance\"<BR>\n" );
document.write( "This is equivalent to 56 months because 12*4+8 = 48+8 = 56.\r<BR>\n" );
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document.write( "Answer:  56 months<BR>\n" );
document.write( "This is equivalent to 4 years, 8 months<BR>\n" );
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