document.write( "Question 967716: How long will it take to earn your first million dollars if you annually invest $1000 into an IRA at 10% interest compounded monthly.
\n" ); document.write( "This answer should be calculated using logarithms so that the answer is exact.
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Algebra.Com's Answer #591482 by MathTherapy(10555)\"\" \"About 
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How long will it take to earn your first million dollars if you annually invest $1000 into an IRA at 10% interest compounded monthly.
\n" ); document.write( "This answer should be calculated using logarithms so that the answer is exact.
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Use Future Value of Ordinary Annuity formula: \"FV%5Boa%5D+=+PMT+%2A+%28%28%281%2Bi%2Fm%29%5E%28mt%29-1%29%2F%28i%2Fm%29%29%29\"
\n" ); document.write( "\"1000000+=+1000+%2A+%28%28%281+%2B+.1%2F12%29%5E%2812t%29+-+1%29%2F%28.1%2F12%29%29%29\"
\n" ); document.write( "\"1000000%2F1000+=+%28%28%281+%2B+.1%2F12%29%5E%2812t%29+-+1%29%2F%28.1%2F12%29%29%29\"
\n" ); document.write( "
\n" ); document.write( "\"1000+=+%28%28%28%2812+%2B+.1%29%2F12%29%5E%2812t%29+-+1%29%2F%28.1%2F12%29%29%29%29\"
\n" ); document.write( "\"1000+=+%28%28%2812.1%2F12%29%5E%2812t%29+-+1%29%2F%28.1%2F12%29%29%29\"
\n" ); document.write( "\"%2812.1%2F12%29%5E%2812t%29+-+1+=+100%2F12\" ------ Cross-multiplying
\n" ); document.write( "\"%2812.1%2F12%29%5E%2812t%29+-+1+=+25%2F3\"
\n" ); document.write( "\"%2812.1%2F12%29%5E%2812t%29+=+25%2F3+%2B+1\"
\n" ); document.write( "\"%2812.1%2F12%29%5E%2812t%29+=+25%2F3+%2B+3%2F3\"
\n" ); document.write( "\"%2812.1%2F12%29%5E%2812t%29+=+28%2F3\" ---------- Exponential form
\n" ); document.write( "\"log+%2812.1%2F12%2C+%2828%2F3%29%29+=+12t\" -------- Logarithmic form
\n" ); document.write( "\"log+%2828%2F3%29%2Flog+%2812.1%2F12%29+=+12t\" ---------- Applying change of base
\n" ); document.write( "\"%28log+%2828%2F3%29%29%2F%28log+%2812.1%2F12%29%29\"\"%22%F7%22\"\"12+=+t\"
\n" ); document.write( "\"highlight_green%28t+=+%28log+%2828%2F3%29%29%2F%2812+%2A+%28log+%2812.1%2F12%29%29%29%29\" years ------ EXACT TIME
\n" ); document.write( "\"highlight_green%28t+=+22.42885983%29\" years ------------ APPROXIMATE TIME \n" ); document.write( "
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