Antonio wants to buy a car but only has half as much money as he needs. If Antonio deposits the money into a savings account that earns $11 \%$ interest compounded continuously, how long will it take for his money to double?

Round your answer to the nearest month.

Step 1 ：The problem is asking for the time it takes for an initial amount of money to double when it's compounded continuously at an interest rate of 11%. This is a problem of continuous compound interest, which can be solved using the formula for continuous compounding: \(A = P * e^{rt}\) where: \(A\) is the final amount of money, \(P\) is the initial amount of money, \(r\) is the interest rate (expressed as a decimal), \(t\) is the time (in years), and \(e\) is the base of the natural logarithm (approximately 2.71828).

Step 2 ：Since Antonio wants his money to double, \(A\) is twice \(P\). Therefore, we can simplify the equation to: \(2P = P * e^{rt}\). Dividing both sides by \(P\) gives: \(2 = e^{rt}\).

Step 3 ：We can then solve for \(t\): \(t = \ln(2) / r\). We know that \(r\) is 11%, or 0.11. We can plug this into the equation to find \(t\).

Step 4 ：Since the problem asks for the answer in months, we'll need to convert \(t\) from years to months by multiplying by 12. \(r = 0.11\), \(t = 6.301338005090412\), \(t_{months} = 75.61605606108495\).

Step 5 ：Rounding \(t_{months}\) to the nearest whole number gives us the final answer: \(\boxed{76}\) months.