document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202635>Question 1202635</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ali invests $14 800 in an account that earns interest compounded semi-annually for 8 years. She then takes all the money, which amounts to $17 063.24, and invests it in an account that earns interest compounded quarterly for 6 years. After the 14 years, the account is worth $18 846.11. What annual interest rate was Ali earning on each of the accounts?  </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( "A = final amount<BR>\n" );
document.write( "P = deposit<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( "Use this given info<BR>\n" );
document.write( "\"<font color=blue>Ali invests $14,800 in an account that earns interest compounded semi-annually for 8 years...which amounts to $17,063.24</font>\"<BR>\n" );
document.write( "to determine:<BR>\n" );
document.write( "A = 17063.24<BR>\n" );
document.write( "P = 14800<BR>\n" );
document.write( "r = unknown<BR>\n" );
document.write( "n = 2<BR>\n" );
document.write( "t = 8\r<BR>\n" );
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document.write( "A = P*(1+r/n)^(n*t)<BR>\n" );
document.write( "17063.24 = 14800*(1+r/2)^(2*8)<BR>\n" );
document.write( "17063.24 = 14800*(1+r/2)^16<BR>\n" );
document.write( "17063.24/14800 = (1+r/2)^16<BR>\n" );
document.write( "1.15292162 = (1+r/2)^16<BR>\n" );
document.write( "(1+r/2)^16 = 1.15292162 <BR>\n" );
document.write( "1+r/2 = (1.15292162)^(1/16) <BR>\n" );
document.write( "1+r/2 = 1.00893337<BR>\n" );
document.write( "r/2 = 1.00893337-1<BR>\n" );
document.write( "r/2 = 0.00893337<BR>\n" );
document.write( "r = 2*0.00893337<BR>\n" );
document.write( "r = 0.01786674<BR>\n" );
document.write( "r = 0.01787<BR>\n" );
document.write( "The first account has an annual rate of about 1.787%\r<BR>\n" );
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document.write( "For the 2nd account, Ali has:<BR>\n" );
document.write( "A = 18846.11<BR>\n" );
document.write( "P = 17063.24<BR>\n" );
document.write( "r = unknown<BR>\n" );
document.write( "n = 4<BR>\n" );
document.write( "t = 6\r<BR>\n" );
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document.write( "Caution: The instructions mention <font color=blue>After the 14 years</font>, but we will not use t = 14 for the 2nd account. <BR>\n" );
document.write( "The money sits in the 2nd account for 6 years and not 14.<BR>\n" );
document.write( "The 14 refers to 8 years + 6 years = 14 years total.\r<BR>\n" );
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document.write( "I'll skip the steps (since they will be similar to the ones shown above), but you should get r = 0.0166 to represent an annual rate of approximately 1.66%<BR>\n" );
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