document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193578>Question 1193578</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with the homework.\r<BR>\n" );
document.write( "\n" );
document.write( "1. The simple discount rate of a bank is 16% per annum if a client signs a note to pay 6000 in nine months time:<BR>\n" );
document.write( "1.1 How much will the client receive?<BR>\n" );
document.write( "1.2. what is the equivalent simple interest of the loan? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848560 by </B><A HREF=/tutors/aboutme.mpl?userid=parmen><B>parmen(42)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=parmen><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=848560\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ### 1.1. Amount the Client Will Receive\r<BR>\n" );
document.write( "\n" );
document.write( "The client signs a note to pay \( M = 6000 \) in nine months. The bank uses a simple discount rate formula:\r<BR>\n" );
document.write( "\n" );
document.write( "\[<BR>\n" );
document.write( "PV = M \times (1 - d \times t)<BR>\n" );
document.write( "\]\r<BR>\n" );
document.write( "\n" );
document.write( "Where:<BR>\n" );
document.write( "- \( M = 6000 \) (maturity value),<BR>\n" );
document.write( "- \( d = 0.16 \) (simple discount rate per annum),<BR>\n" );
document.write( "- \( t = \frac{9}{12} = 0.75 \) years (time until maturity).\r<BR>\n" );
document.write( "\n" );
document.write( "Substituting:\r<BR>\n" );
document.write( "\n" );
document.write( "\[<BR>\n" );
document.write( "PV = 6000 \times (1 - 0.16 \times 0.75)<BR>\n" );
document.write( "\]\r<BR>\n" );
document.write( "\n" );
document.write( "\[<BR>\n" );
document.write( "PV = 6000 \times (1 - 0.12)<BR>\n" );
document.write( "\]\r<BR>\n" );
document.write( "\n" );
document.write( "\[<BR>\n" );
document.write( "PV = 6000 \times 0.88<BR>\n" );
document.write( "\]\r<BR>\n" );
document.write( "\n" );
document.write( "\[<BR>\n" );
document.write( "PV = 5280<BR>\n" );
document.write( "\]\r<BR>\n" );
document.write( "\n" );
document.write( "The client will receive **R5280**.\r<BR>\n" );
document.write( "\n" );
document.write( "---\r<BR>\n" );
document.write( "\n" );
document.write( "### 1.2. Equivalent Simple Interest of the Loan\r<BR>\n" );
document.write( "\n" );
document.write( "To find the equivalent simple interest, we first determine the **interest amount** and then calculate the equivalent simple interest rate (\( r \)).\r<BR>\n" );
document.write( "\n" );
document.write( "#### Interest Amount:<BR>\n" );
document.write( "\[<BR>\n" );
document.write( "\text{Interest} = M - PV = 6000 - 5280 = 720<BR>\n" );
document.write( "\]\r<BR>\n" );
document.write( "\n" );
document.write( "#### Equivalent Simple Interest Formula:<BR>\n" );
document.write( "\[<BR>\n" );
document.write( "\text{Interest} = PV \times r \times t<BR>\n" );
document.write( "\]\r<BR>\n" );
document.write( "\n" );
document.write( "Rearranging for \( r \):\r<BR>\n" );
document.write( "\n" );
document.write( "\[<BR>\n" );
document.write( "r = \frac{\text{Interest}}{PV \times t}<BR>\n" );
document.write( "\]\r<BR>\n" );
document.write( "\n" );
document.write( "Substitute the values:\r<BR>\n" );
document.write( "\n" );
document.write( "\[<BR>\n" );
document.write( "r = \frac{720}{5280 \times 0.75}<BR>\n" );
document.write( "\]\r<BR>\n" );
document.write( "\n" );
document.write( "\[<BR>\n" );
document.write( "r = \frac{720}{3960}<BR>\n" );
document.write( "\]\r<BR>\n" );
document.write( "\n" );
document.write( "\[<BR>\n" );
document.write( "r \approx 0.1818 \, \text{or } 18.18\%<BR>\n" );
document.write( "\]\r<BR>\n" );
document.write( "\n" );
document.write( "The equivalent simple interest rate is **18.18% per annum**.\r<BR>\n" );
document.write( "\n" );
document.write( "---\r<BR>\n" );
document.write( "\n" );
document.write( "### Final Summary:\r<BR>\n" );
document.write( "\n" );
document.write( "1. **Amount Received by the Client**: \( R5280 \)<BR>\n" );
document.write( "2. **Equivalent Simple Interest Rate**: \( 18.18\% \) per annum </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );