document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198963>Question 1198963</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Frank invests $3500 dollars into an account earning interest compounded quarterly. After 10 years there is $5050 in the account. What was the interest rate? </SPAN>\n" );
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document.write( "Compound interest formula<BR>\n" );
document.write( "A = P*(1+r/n)^(n*t)\r<BR>\n" );
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document.write( "Variables:<BR>\n" );
document.write( "A = final account value after t years<BR>\n" );
document.write( "P = deposit or starting value<BR>\n" );
document.write( "r = annual interest rate in decimal form<BR>\n" );
document.write( "n = compounding frequency<BR>\n" );
document.write( "t = number of years \r<BR>\n" );
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document.write( "In this case:<BR>\n" );
document.write( "A = 5050<BR>\n" );
document.write( "P = 3500<BR>\n" );
document.write( "r = unknown<BR>\n" );
document.write( "n = 4<BR>\n" );
document.write( "t = 10\r<BR>\n" );
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document.write( "Let's solve for the variable r.<BR>\n" );
document.write( "A = P*(1+r/n)^(n*t)<BR>\n" );
document.write( "5050 = 3500*(1+r/4)^(4*10)<BR>\n" );
document.write( "5050/3500 = (1+r/4)^(40)<BR>\n" );
document.write( "1.442857143 = (1+r/4)^(40)<BR>\n" );
document.write( "(1+r/4)^(40) = 1.442857143<BR>\n" );
document.write( "1+r/4 = (1.442857143)^(1/40)<BR>\n" );
document.write( "1+r/4 = 1.009207765<BR>\n" );
document.write( "r/4 = 1.009207765 - 1<BR>\n" );
document.write( "r/4 = 0.009207765<BR>\n" );
document.write( "r = 4*0.009207765<BR>\n" );
document.write( "r = 0.03683106<BR>\n" );
document.write( "r = 0.0368\r<BR>\n" );
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document.write( "r*(100%) = 0.0368*100% = 3.68%<BR>\n" );
document.write( "In other words, we move the decimal point two spots to the right to go from 0.0368 to 3.68%\r<BR>\n" );
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document.write( "The annual interest rate is roughly <font color=red>3.68%</font>\r<BR>\n" );
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document.write( "To verify the answer, we can use a TVM calculator such as this<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.geogebra.org/m/mvv2nus2\">https://www.geogebra.org/m/mvv2nus2</a><BR>\n" );
document.write( "A similar feature is found on any TI83 or TI84 calculator.<BR>\n" );
document.write( "TVM = time value of money\r<BR>\n" );
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document.write( "The input values are<BR>\n" );
document.write( "N = 10<BR>\n" );
document.write( "I% = left blank<BR>\n" );
document.write( "PV = -3500<BR>\n" );
document.write( "PMT = 0<BR>\n" );
document.write( "FV = 5050<BR>\n" );
document.write( "P/Y = 1<BR>\n" );
document.write( "C/Y = 4\r<BR>\n" );
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document.write( "N represents the number of periods. In this case it's the number of years.<BR>\n" );
document.write( "PV is negative to represent a cash outflow.<BR>\n" );
document.write( "PMT represents the periodic payment. We type zero here to indicate we don't have periodic payments; rather we have a one-time deposit instead.<BR>\n" );
document.write( "C/Y stands for \"compoundings per year\"\r<BR>\n" );
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document.write( "After you input those items into the proper boxes, press the \"solve for I%\" button to have <font color=red>3.68</font> show up in that box.\r<BR>\n" );
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document.write( "Answer: <font color=red>3.68%</font> (approximate)\r<BR>\n" );
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document.write( "Another similar finance question that involves TVM:<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1199059.html\">https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1199059.html</a><BR>\n" );
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