document.write( "Question 1183163: Suppose you have $8000 deposited in an account with interest compounded semiannually. After 8 years, the account has grown to $9300. What is the interest rate on this account? (Round your answer to the nearest hundredth of a percent) \n" ); document.write( "

Algebra.Com's Answer #813336 by ikleyn(52800) $\"\"$ $\"About$

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\n" ); document.write( "Suppose you have $8000 deposited in an account with interest compounded semiannually.
\n" ); document.write( "After 8 years, the account has grown to $9300. What is the interest rate on this account?
\n" ); document.write( "(Round your answer to the nearest hundredth of a percent)
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document.write( "Your starting equation is\r\n" );
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document.write( "    9300 = \r\n" );
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document.write( "and your goal is to find the unknown annual interest rate r (as decimal).\r\n" );
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document.write( "You simplify your equation\r\n" );
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document.write( "     = ,\r\n" );
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document.write( "    1.1625 = .\r\n" );
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document.write( "You take logarithm base 10 from both sides\r\n" );
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document.write( "    log(1.1625) = 16*log(1+r/2)\r\n" );
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document.write( "and find\r\n" );
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document.write( "     =  = 0.004087.\r\n" );
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document.write( "Next, you take exponent of both sides and get\r\n" );
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document.write( "     =  = 1.009455.\r\n" );
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document.write( "Hence,\r\n" );
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document.write( "    r/2 = 1.009455 - 1 = 0.009455;   r = 2*0.009455 = 0.01891.\r\n" );
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document.write( "Thus the annual percentage compound rate is 1.89%.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "To see many other similar (and different) solved problems, look into the lesson\r
\n" ); document.write( "\n" ); document.write( " - Problems on discretely compound accounts \r
\n" ); document.write( "\n" ); document.write( "in this site, and learn the subject from there.\r
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\n" ); document.write( "\n" ); document.write( "After reading this lesson, you will tackle such problems on your own without asking for help from outside.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( " - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic \"Logarithms\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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\n" ); document.write( "\n" ); document.write( "Happy learning (!)\r
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