document.write( "Question 625774: How long will it take for $8000 to double at a compounding rate of 2% paid daily? A second and third doubling figure would be appreciated. Can you please tell me the formula for computing this problem. \n" ); document.write( "
Algebra.Com's Answer #393897 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
without getting into the derivation of it, the formula for doubling 8000 assuming you are earning interest compounded at 2% per day is:
\n" ); document.write( "y = x * (1.02)^(log(2) / log(1.02))
\n" ); document.write( "if x is 8000, then y equals 16000
\n" ); document.write( "if x is 16000, then y equals 32000, etc.
\n" ); document.write( "since log(2) / log(1.02)) is equal to 35.00278878, you can use an exponent of:
\n" ); document.write( "35 rounded to the nearest integer.
\n" ); document.write( "35.003 rounded to the nearest 3 decimal places.
\n" ); document.write( "35.0028 rounded to the nearest 4 decimal places.
\n" ); document.write( "35.00279 rounded to the nearest 5 decimal places.
\n" ); document.write( "suppose you used 35 (that would be 35 days).
\n" ); document.write( "your formula would be:
\n" ); document.write( "8000 * 1.02^35 = 15999.11642
\n" ); document.write( "that's pretty close.
\n" ); document.write( "let's say that z = log(2)/log(1.02)
\n" ); document.write( "your formula becomes:
\n" ); document.write( "y = x*1.02^z
\n" ); document.write( "that's the formula you use.
\n" ); document.write( "you can make z as accurate as you want it.
\n" ); document.write( "the most accurate is to plug solve for z = log(2)/log(2.01) in your calculator and then stores the result in memory and then use that memory time you need z.
\n" ); document.write( "the daily interest rate is 2%
\n" ); document.write( "the money you make each day is compounded and calculated as the principal for the interest calculated for the next day, etc.\r
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