document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1172633>Question 1172633</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Kindly help again<BR>\n" );
document.write( "1. How long it will take for R6000 invested at 6% p.a.simple interest to grow to R8520.<BR>\n" );
document.write( "2.Calculate compound interest earned of R15000 deposited into bank for 2 years at 12%p.a </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #797729 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=797729\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. How long it will take for R6000 invested at 6% p.a.simple interest to grow to R8520.\r<BR>\n" );
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document.write( "simple interest formula is:<BR>\n" );
document.write( "f = p + p * r * t<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( "t is the number of time periods.\r<BR>\n" );
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document.write( "in your problem, this becomes:<BR>\n" );
document.write( "f = 6000 + 6000 * .06 * t<BR>\n" );
document.write( "since f = 8520, this becomes:<BR>\n" );
document.write( "8520 = 6000 + 6000 * .06 * t<BR>\n" );
document.write( "subtract 6000 from both sides of the equation to get:<BR>\n" );
document.write( "2520 = 6000 * .06 * t<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "2520 = 360 * t<BR>\n" );
document.write( "solve for t to get:<BR>\n" );
document.write( "t = 2520 / 360 = 7\r<BR>\n" );
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document.write( "it will take 7 years for 6000 to grow to 8520 at 6% per year.<BR>\n" );
document.write( "confirm by going back to the formula to get:<BR>\n" );
document.write( "f = p + p * r * t becomes:<BR>\n" );
document.write( "8520 = 6000 + 6000 * .06 * 7 which becomes:<BR>\n" );
document.write( "8520 = 6000 + 360 * 7 which becomes:<BR>\n" );
document.write( "8520 = 8520<BR>\n" );
document.write( "this confirms the solution is correct.\r<BR>\n" );
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document.write( "2. Calculate compound interest earned of R15000 deposited into bank for 2 years at 12%p.a\r<BR>\n" );
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document.write( "the compound interest formula is:<BR>\n" );
document.write( "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" );
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document.write( "in your problem, the formula becomes:<BR>\n" );
document.write( "f = 15000 * (1 + .12) ^ 2<BR>\n" );
document.write( "solve for f to get:<BR>\n" );
document.write( "f = 18816\r<BR>\n" );
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document.write( ".12 was the interest rate per year.<BR>\n" );
document.write( "2 was the number of years.<BR>\n" );
document.write( "annual compounding was assumed.\r<BR>\n" );
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document.write( "since this was only 2 years, it is easy to show the details.\r<BR>\n" );
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document.write( "in time period 0, you have 15000<BR>\n" );
document.write( "in time period 1, you multiply 15000 * 1.12 to get 16800<BR>\n" );
document.write( "in time period 2, you multiply 16800 * 1.12 to get 18816.\r<BR>\n" );
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document.write( "the difference between simple interest and compound interest is that, ...<BR>\n" );
document.write( "in simple interest, the interest is calculated off the original principle.<BR>\n" );
document.write( "in compound interest, the interest is calculate off the principal plus interest from the preceding time period.\r<BR>\n" );
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document.write( "to show you the difference, in your second principle, if it was simple interest, the calculations would have been:\r<BR>\n" );
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document.write( "f = 15000 + 15000 * .12 * 2 = 18600\r<BR>\n" );
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document.write( "the details for that would be:\r<BR>\n" );
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document.write( "in time period, you have 15000.<BR>\n" );
document.write( "in time period 1, you have 15000 + .12 * 15000 = 16800<BR>\n" );
document.write( "in time period 3, you have 16800 + .12 * 15000 = 18600\r<BR>\n" );
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document.write( "with compound interest, you earned interest on interest.<BR>\n" );
document.write( "with simple interest, you earned interest on the original amount only.\r<BR>\n" );
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document.write( "let me know if you have any questions concerning this.<BR>\n" );
document.write( "theo\r<BR>\n" );
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document.write( " </SPAN>\n" );
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