document.write( "Question 1102179: Find the effective rate of interest for 6% compounded monthly and 6% compounded continuously.\r
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document.write( "First 6% is 0.06 and the equations used are
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document.write( "Compounded Continuously
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document.write( "Compounded Monthly
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document.write( "For Monthly I did
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document.write( "and got as my answer \r
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document.write( "For Continuously I did
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document.write( "and got 6.184% as my answer \r
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document.write( "I just wanted to check if these were ok or if I did steps wrong, thank you!
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Algebra.Com's Answer #716839 by Theo(13342)![]() ![]() You can put this solution on YOUR website! you basically find the future value of the present amount of 1 for 1 year at the indicated compounding rate.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "you then subtract 1 from that to get the effective interest rate.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "your monthly compounding formula is:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "A = p * (1 + r/n) ^ nt\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "A is the future value \n" ); document.write( "p is the present value \n" ); document.write( "r is the interest rate per year \n" ); document.write( "n is the number of compounding periods per year \n" ); document.write( "t is the number of years\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "with monthly compounding at 6% per year with p = 1 and t = 1, the formula becomes:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "A = (1 + .06/12) ^ 12\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "solve for A to get A = 1.005 ^ 12 = 1.061677812\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "subtract 1 from A to get effective interest rate = .061677812 per year which is equal to 6.1678812% per year.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "your continuous compounding formula is:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "A = p * e ^ rt\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "A is the future value \n" ); document.write( "p is the present value \n" ); document.write( "r is the interest rate per year \n" ); document.write( "t is the number of years\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "when p = 1 and t = 1 and r = .06, the formula becomes:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "A = e ^ .06\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "solve for A to get A = 1.061836547\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "subtract 1 from A to get effective interest rate = .061836547 per year which is equal to 6.1836547% per year.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "it looks like you did it ok with some minor differences between the way your presented your results and the way i presented mine.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "if you're looking for the effective interest rate per year, then t should be equal to 1.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "making p equal to 1 allows you to find 1 plus the interest rate.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "subtracting 1 from that gets you the interest rate.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "i would say you did ok.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |