document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178048>Question 1178048</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The hire purchase price of a refrigerator is 6000. The deposit of 500 is made and the remainder is paid in equal monthly payments of 2500.\r<BR>\n" );
document.write( "\n" );
document.write( "a) if the cash price is 4000, express as a percentage of the cash price, the extra cost of buying on hire purchase.\r<BR>\n" );
document.write( "\n" );
document.write( "b) what is the interest rate (simple interest) charged on this transaction  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850373 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850373\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's solve this problem step-by-step.\r<BR>\n" );
document.write( "\n" );
document.write( "**a) Extra Cost of Hire Purchase**\r<BR>\n" );
document.write( "\n" );
document.write( "1.  **Calculate the Total Amount Paid in Installments:**<BR>\n" );
document.write( "    * Hire purchase price: 6000<BR>\n" );
document.write( "    * Deposit: 500<BR>\n" );
document.write( "    * Amount paid in installments: 6000 - 500 = 5500\r<BR>\n" );
document.write( "\n" );
document.write( "2.  **Calculate the Extra Cost:**<BR>\n" );
document.write( "    * Cash price: 4000<BR>\n" );
document.write( "    * Total amount paid on hire purchase: 500 (deposit) + 5500 (installments) = 6000<BR>\n" );
document.write( "    * Extra cost: 6000 - 4000 = 2000\r<BR>\n" );
document.write( "\n" );
document.write( "3.  **Express as a Percentage of the Cash Price:**<BR>\n" );
document.write( "    * Percentage extra cost = (Extra cost / Cash price) * 100<BR>\n" );
document.write( "    * Percentage extra cost = (2000 / 4000) * 100 = 0.5 * 100 = 50%\r<BR>\n" );
document.write( "\n" );
document.write( "**Therefore, the extra cost of buying on hire purchase is 50% of the cash price.**\r<BR>\n" );
document.write( "\n" );
document.write( "**b) Interest Rate (Simple Interest)**\r<BR>\n" );
document.write( "\n" );
document.write( "1.  **Calculate the Total Interest Paid:**<BR>\n" );
document.write( "    * Total interest = 2000 (from part a)\r<BR>\n" );
document.write( "\n" );
document.write( "2.  **Determine the Number of Installments:**<BR>\n" );
document.write( "    * Amount paid in installments: 5500<BR>\n" );
document.write( "    * Monthly payment: 2500<BR>\n" );
document.write( "    * Number of installments: 5500 / 2500 = 2.2. This indicates that there are two full payments and a partial payment. Therefore there are 3 payments.\r<BR>\n" );
document.write( "\n" );
document.write( "3.  **Calculate the Time Period:**<BR>\n" );
document.write( "    * Since there are 3 payments, the time period is 3 months.\r<BR>\n" );
document.write( "\n" );
document.write( "4.  **Calculate the Principal:**<BR>\n" );
document.write( "    * The principal is the cash price minus the deposit: 4000 - 500 = 3500\r<BR>\n" );
document.write( "\n" );
document.write( "5.  **Use the Simple Interest Formula:**<BR>\n" );
document.write( "    * Simple Interest (I) = Principal (P) * Rate (R) * Time (T)<BR>\n" );
document.write( "    * 2000 = 3500 * R * (3/12) (Time is in years, so 3 months = 3/12 years)<BR>\n" );
document.write( "    * 2000 = 3500 * R * 0.25<BR>\n" );
document.write( "    * 2000 = 875 * R<BR>\n" );
document.write( "    * R = 2000 / 875 ≈ 2.2857\r<BR>\n" );
document.write( "\n" );
document.write( "6.  **Convert to Percentage:**<BR>\n" );
document.write( "    * R ≈ 2.2857 * 100 = 228.57% per year\r<BR>\n" );
document.write( "\n" );
document.write( "**Therefore, the simple interest rate charged on this transaction is approximately 228.57% per year.**<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );