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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.
Answer by Theo(13342)   (Show Source):
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:
y = x * (1.02)^(log(2) / log(1.02))
if x is 8000, then y equals 16000
if x is 16000, then y equals 32000, etc.
since log(2) / log(1.02)) is equal to 35.00278878, you can use an exponent of:
35 rounded to the nearest integer.
35.003 rounded to the nearest 3 decimal places.
35.0028 rounded to the nearest 4 decimal places.
35.00279 rounded to the nearest 5 decimal places.
suppose you used 35 (that would be 35 days).
your formula would be:
8000 * 1.02^35 = 15999.11642
that's pretty close.
let's say that z = log(2)/log(1.02)
your formula becomes:
y = x*1.02^z
that's the formula you use.
you can make z as accurate as you want it.
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.
the daily interest rate is 2%
the money you make each day is compounded and calculated as the principal for the interest calculated for the next day, etc.
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