document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=996409>Question 996409</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Bank 'A' provides loan at 5% per annum at simple interest and bank 'B' provides loan at the same rate for the same period compounded annually. Then, which bank is preferable for a person to take a loan? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #614870 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=614870\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the bank that compounds annually is the better choice because you are earning interest on interest.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "formula for future value of a present amount for n years assuming simple interest is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f = p * (1 + x*n)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "formula for future value of a present amount for n year at x interest rate assuming annual compounding is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f = p * (1+x)^n\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for example:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "assume 1000 investment at 5% per year.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simple interest gets you:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f = 1000 * (1+.05*5) = 1250\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "compound interest gets you:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f = 1000 * (1+.05)^5 = 1276.28\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "with simple interest, the interest each year is calculated off the original investment * the interest rate.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you get 1000 + 1000*.05 + 1000*.05 + 1000*.05 + 1000*.05 + 1000*.05\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "total interest = 50 + 50 + 50 + 50 + 50 = 250\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "with compound interest. the interest rate each year is calculated off the original investment plus the total interest earned the previous year.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you get 1000 + 1000*.05 + 1050*.05 + 1102.5*.05 + 1157.625*.05 + 1215.50625*.05\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "total interest = 50 + 52.5 + 55.125 + 57.88125 + 60.7753125 = 276.2815625\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );