Question 1040435
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P = Initial amount deposited = 5400
A = final amount after t years = 2*5400 = 10800
r = interest rate in decimal form = 0.033
t = time in years = unknown


We're using this formula

{{{A = P*e^(r*t)}}}

where 'e' is a constant (e = 2.718... approx. It's similar to pi = 3.14...)



Let's use the values given above to find t



{{{A = P*e^(r*t)}}}



{{{10800 = 5400*e^(0.033*t)}}}



{{{10800/5400 = (5400*e^(0.033*t))/5400}}}



{{{2 = e^(0.033*t)}}}



{{{e^(0.033*t) = 2}}}



{{{0.033t = ln(2)}}}



{{{t = ln(2)/0.033}}}



{{{t = 21.004460016968}}}



It will take approximately 21.004460016968 years.



Round that to the nearest tenth to get the final answer of <font color=red size=5>21.0 years</font>



Side note: Using the rule of 72, we'd have 72/x = 72/3.3 = 21.8181818181819 which is fairly close to what we got above. So this rule will give you a quick idea of the approximate doubling time. 
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