document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1148818>Question 1148818</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Delaney took out a $32,000 student loan with a fixed interest rate to pay for college. Delaney did not make payments on her loan for a period of 7 years. After this time period interest had accrued, resulting in the loan balance increasing to $60,000.\r<BR>\n" );
document.write( "\n" );
document.write( "What is is the 7-year growth factor for the amount that Delaney owes on the loan?\r<BR>\n" );
document.write( "\n" );
document.write( "1.7483<BR>\n" );
document.write( "Incorrect   \r<BR>\n" );
document.write( "\n" );
document.write( "What is the 7-year percent change for the amount that Delaney owes on the loan?\r<BR>\n" );
document.write( "\n" );
document.write( "74<BR>\n" );
document.write( "Incorrect %   \r<BR>\n" );
document.write( "\n" );
document.write( "What is is the 1-year growth factor for the amount that Delaney owes on the loan?\r<BR>\n" );
document.write( "\n" );
document.write( "1.81<BR>\n" );
document.write( "Incorrect   \r<BR>\n" );
document.write( "\n" );
document.write( "What is the 1-year percent change for the amount that Delaney owes on the loan?\r<BR>\n" );
document.write( "\n" );
document.write( "Incorrect %   \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #770172 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=770172\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 60,000 / 32,000 = 1.875<BR>\n" );
document.write( "that should be your 7 year growth factor.<BR>\n" );
document.write( "you multiply 32,000 by 1.875 and you get 60,000.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "multiply that by 100 to get the 7 year percent change factor.<BR>\n" );
document.write( "that would be 187.5%.<BR>\n" );
document.write( "the amount owed grew 187.5%.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the 1 year growth factor would be found as follows, using the general formula for growth of f = p * (1 + r) ^ n<BR>\n" );
document.write( "f is the future value.<BR>\n" );
document.write( "p is the present value.<BR>\n" );
document.write( "r is the interest rate per time period.<BR>\n" );
document.write( "n is the number of time periods.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the formula becomes 60,000 = 32,000 * (1 + r) ^ 7<BR>\n" );
document.write( "divide both sides of this formula by 32,000 to get:<BR>\n" );
document.write( "60,000 / 32,000 = (1 + r) ^ 7<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "1.875 = (1 + r) ^ 7\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the 1.875 is your growth factor.<BR>\n" );
document.write( "take the 7th root of each side of that equation to get:<BR>\n" );
document.write( "1.875 ^ (1/7) = 1 + r<BR>\n" );
document.write( "solve for 1 + r to get:<BR>\n" );
document.write( "1 + r = 1.093956824.<BR>\n" );
document.write( "that's your 1 year growth factor.<BR>\n" );
document.write( "32,000 grows by that factor each year for 7 years to get:<BR>\n" );
document.write( "32,000 * 1.093956824 ^ 7 = 60,000.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "multiply that by 100 to get the 1 year percent change of 109.3956824%.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your answers could be:<BR>\n" );
document.write( "1.875<BR>\n" );
document.write( "187.5%<BR>\n" );
document.write( "1.093956824<BR>\n" );
document.write( "109.3956824%\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "or they could be:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( ".875<BR>\n" );
document.write( "87.5%<BR>\n" );
document.write( ".093956824<BR>\n" );
document.write( "9.3956824%\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "it all depends on what they mean by a growth factor or a growth percent.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for example:<BR>\n" );
document.write( "it's true that 32,000 * 1.875 = 60,000<BR>\n" );
document.write( "you can also say that 32,000 grow by a factor of .875.<BR>\n" );
document.write( "in that case you would mean that you multiply 32,000 by .875 and then add that to the original amount to get 60,000.<BR>\n" );
document.write( "32,000 * .875 = 28,000 + 32,000 = 60,000\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "32,000 * 1.875 is equivalent to 32,000 * (1 + .875) which is equivalent to 32,000 * 1 + 32,000 * .875.<BR>\n" );
document.write( "the growth factor could be viewed as 1.875 or it could be viewed as .875.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "same goes for the growth percent.<BR>\n" );
document.write( "i said it was 187.5%.<BR>\n" );
document.write( "it could be viewed as .875 * 100 = 87.5%.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "same goes for the 1 year growth factor.<BR>\n" );
document.write( "it could be viewed as 1.093956824 or it could be viewed as .093956824.<BR>\n" );
document.write( "60,000 = 32,000 * 1.093956824 ^ 7 is equivalent to 32,000 * (1 + .093956824) ^ 7 <BR>\n" );
document.write( "after you divide both sides of that equation by 32,000, and, when you take the seventh root of both sides of that equation, you get:<BR>\n" );
document.write( "(60,000 / 32,000) ^ (1/7) = (1 + r)<BR>\n" );
document.write( "you then solve for (1 + r) = 1.093956824.<BR>\n" );
document.write( "you then subtract 1 from both sides of that equation to get:<BR>\n" );
document.write( "r = .093956824.<BR>\n" );
document.write( "that is the annual rate of growth.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if they're looking for the growth factor and the percent change as you had shown them, then the third possible set of answers would be:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1.875<BR>\n" );
document.write( "87.5%<BR>\n" );
document.write( "1.093956824<BR>\n" );
document.write( "9.3956824%.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you would round as required.<BR>\n" );
document.write( "give it a shot and see how it goes.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );