document.write( "Question 1206609: You deposit $6000 into an account that earns 7% compounded annually. A friend deposits $5500 into an account that earns 6.95% annual interest, compounded continuously. Will your friend's balance ever equal yours? If so, when? If not, enter NEVER.
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Algebra.Com's Answer #844171 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "You deposit $6000 into an account that earns 7% compounded annually.
\n" ); document.write( "A friend deposits $5500 into an account that earns 6.95% annual interest, compounded continuously.
\n" ); document.write( "Will your friend's balance ever equal yours? If so, when? If not, enter NEVER.
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document.write( "For your account, the effective annual growth coefficient is 1.07.\r\n" );
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document.write( "For your friend's account, the effective annual growth coefficient is \r\n" );
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document.write( "     =  = 1.071972011.\r\n" );
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document.write( "As you see, for your friend's account, the effective annual coefficient is greater than your, \r\n" );
document.write( "so the friend's account is growing faster and will catch with your account somewhen.\r\n" );
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document.write( "To find this catching time moment , write an equation\r\n" );
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document.write( "     = .\r\n" );
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document.write( "It gives\r\n" );
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document.write( "     = ,\r\n" );
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document.write( "    1.090909091 = , \r\n" );
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document.write( "    1.090909091 = .\r\n" );
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document.write( "Take logarithm base 10 of both sides\r\n" );
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document.write( "    log(1.090909091) = log(1.001843001)*t\r\n" );
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document.write( "and find t\r\n" );
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document.write( "    t =  = 47.25528282 years.\r\n" );
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document.write( "Now round 47.25528282 to the closest greater integer year and get the\r\n" );
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document.write( "ANSWER. Your friend's account will be greater than yours in 48 years.\r\n" );
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document.write( "I rounded 47.25528282 to 48 years in order for the bank be able to make the last compounding \r\n" );
document.write( "with your account to compare the accounts in the same time moment in equal conditions.\r\n" );
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