document.write( "Question 1198853: Your parents will retire in 18 years. They currently have $250,000, and they think they will need
\n" ); document.write( "$1 million at retirement. What annual interest rate must they earn to reach their goal, assuming
\n" ); document.write( "they don’t save any additional fund? \n" ); document.write( "
Algebra.Com's Answer #832504 by Theo(13342)\"\" \"About 
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formula to use is f = p * (1 + r) ^ n
\n" ); document.write( "f is the future value
\n" ); document.write( "p is the present value
\n" ); document.write( "(1 + r) is the annual growth rate.
\n" ); document.write( "n is the number of years.\r
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\n" ); document.write( "\n" ); document.write( "formula becomes:
\n" ); document.write( "1,000,000 = 250,000 * (1 + r) ^ 18
\n" ); document.write( "divide both sides of the equation by 250,000 to get:
\n" ); document.write( "4 = (1 + r) ^ 18
\n" ); document.write( "take the 18th root of both sides of the equation to get:
\n" ); document.write( "4 ^ (1/18) = (1 + r)
\n" ); document.write( "solve for (1 + r) to get:
\n" ); document.write( "1 + r = 1.080059739
\n" ); document.write( "that's the annual growth rate.\r
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\n" ); document.write( "\n" ); document.write( "confirm by replacing (1 + r) in the equation with that to get:
\n" ); document.write( "f = 250,000 * 1.080059739 ^ 18 = 1,000,000
\n" ); document.write( "this confirms the value of (1 + 4) is correct.\r
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\n" ); document.write( "\n" ); document.write( "1 + r is the annual growth factor.
\n" ); document.write( "subtract 1 from that to get the annual growth rte.
\n" ); document.write( "that would be .080059739.
\n" ); document.write( "multiply that by 100 and round to decimal places to get 8.01% growth rate per year.
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