document.write( "Question 1050330: Suppose that P dollars in principal is invested in an account that earns compound interest annually and grows to A dollars in t years. The annual interest rate r is given by r = (A/P)^(1/t) - 1. \r
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document.write( "A. Determine the annual interest rate if $2000 grows to $2375.37 after 5 yr.
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document.write( "B. If $5000 is invested at at 5% determine the amount in the account after 6 yr. \n" );
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Algebra.Com's Answer #666046 by Theo(13342)![]() ![]() You can put this solution on YOUR website! problem statement has been reworded below:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Suppose that p dollars in principal is invested in an account that earns compound interest annually and grows to a dollars in t years. The annual interest rate r is given by r = (a/p)^(1/t) - 1. \r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "A. Determine the annual interest rate if $2000 grows to $2375.37 after 5 yr.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "formula to find r is:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "r = a/p ^ (1/t) - 1\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "in this formula:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "a = 2375.37 \n" ); document.write( "p = 2000 \n" ); document.write( "t = 5\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "formula becomes:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "r = (2375.37/2000) ^ (1/5) - 1\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "use your calculator to solve for r to get r = .0348886624.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "B. If $5000 is invested at at 5% determine the amount in the account after 6 yr.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "to determine the amount in the account after 5 years, you have to solve for a.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "the formula you are given is r = (a/p)^(1/t) - 1\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "add 1 to both sides of this equation to get 1+r1 = (a/p)^(1/t)\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "raise both sides of this equation to the power of t to get:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "(1+r)^t = a/p\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "note that ((a/p)^(1/t))^t is equal to (a/p)^(1/t * t) which is equal to (a/p)^1 which is equal to a/p.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "multiply both sides of this equation by p to get:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "p * (1+r)^t = a.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "you are given that:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "p = 5000 \n" ); document.write( "r = .05 \n" ); document.write( "t = 6\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "formula becomes:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "5000 * (1.05)^6 = a\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "solve for a to get:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "a = 5000 * (1.05)^6 = 6700.478203.\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( " \n" ); document.write( " |