document.write( "Question 1114145: a) Grace invests £250,000 at a 6.5% interest rate annually. Compounding the interest annually, how long will it take his investment to double? \n" ); document.write( "
Algebra.Com's Answer #729152 by Theo(13342)\"\" \"About 
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if he doubles his investment, then the future value is 250,000 * 2 = 500,000.\r
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\n" ); document.write( "\n" ); document.write( "the formula to use is f = p * (1+r)^n\r
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\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 year
\n" ); document.write( "n is the number of yers.\r
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\n" ); document.write( "\n" ); document.write( "formula becomes 500,000 = 250,000 * (1 + .065) ^ n\r
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\n" ); document.write( "\n" ); document.write( "divide both sides of this formula by 250,000 and you get 2 = (1 + .065) ^ n\r
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\n" ); document.write( "\n" ); document.write( "take the log of both sides of this euation and you get log(2) = log((1 + .065) ^ n)\r
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\n" ); document.write( "\n" ); document.write( "this is equivalent to log(2) = n * log(1 + .065)\r
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\n" ); document.write( "\n" ); document.write( "divide both sides of this equation by log(1 + .065) and solve for n to get n = log(2) / log(1 + .065).\r
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\n" ); document.write( "\n" ); document.write( "this makes n = 11.00673904\r
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\n" ); document.write( "\n" ); document.write( "the money will double in 11.00673904 years.\r
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\n" ); document.write( "\n" ); document.write( "250,000 * (1 + .065) ^ 11.00673904 = 500,000.\r
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\n" ); document.write( "\n" ); document.write( "11.00673904 years is your answer.\r
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