document.write( "Question 1104551: Please help me solve this word problem:\r
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document.write( "in 1991, the average cost of attending a public university through graduation. Was $20,972. If johns parents deposited that amount in an account in 1991 at an interest rate of 7% compounded semi-annually, how long will it take for the money to double? Round answer to two decimals. \n" );
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Algebra.Com's Answer #720200 by Theo(13342)![]() ![]() You can put this solution on YOUR website! the formula to use is f = p * (1 + r) ^ n\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "f is the future value. \n" ); document.write( "p is the present value. \n" ); document.write( "r is the interest rate per time period. \n" ); document.write( "n is the number of time periods.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "your time periods are in semi-annual periods which means 2 time periods per year.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "your present value is 20792. \n" ); document.write( "your future value is 2 * 20792. \n" ); document.write( "your interest rate per time period is .07 per year / 2 time periods per year = .035. \n" ); document.write( "your number of time periods is n.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "the formula becomes 2 * 20792 = 20792 * (1.035) ^ n.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "divide both sides of this equation by 20792 to get 2 = 1.035 ^ n.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "take the log of both sides of this equation to get log(2) = log(1.035 ^ n).\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "since log(1.035 ^ n) is equal to n * log(1.035), this equation becomes log(2) = n * log(1.035).\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "divide both sides of this equation by log(1.035) to get log(2) / log(1.035) = n.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "solve for n to get n = log(2) / log(1.035) = 20.14879168 time periods.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "since there are 2 time periods per year, then it will take 20.14879168 / 2 = 10.07439584 years.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "round this to 2 decimal places, and it will take 10.07 years.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |