SOLUTION: When interest is compounded continuously, the balance in an account after t years is given by A = Pert,where P is the initial investment and r is the interest rate. Maya has depo

Question 332247: When interest is compounded continuously, the balance in an account after t years is given by A = Pert,where P is the initial investment and r is the interest rate.
Maya has deposited $600 in an account that pays 5.64% interest, compounded continuously. How long will it take for her money to double?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Since we want to double her money, this means that we want 600*2=1200 in return. So . Because "Maya has deposited $600 in an account that pays 5.64% interest", this means that and (the decimal equivalent of 5.64%)

Start with the continuous compounding formula.

Plug in , , and .

Divide both sides by .

Evaluate to get .

Take the natural log of both sides.

Pull down the exponent using the identity .

Evaluate the natural log of 'e' to get 1.

Multiply and simplify.

Evaluate the natural log of to get (this value is approximate).

Divide both sides by to isolate 't'.

Evaluate to get .

Flip the equation.

So in about 12.29 years, her money will double.

Note: her money will double in 12.29 years at a rate of 5.64% regardless of how much she puts in her account. She could invest $2 or $200 and it will still double.
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