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

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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) About Me  (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 A=1200. Because "Maya has deposited $600 in an account that pays 5.64% interest", this means that P=600 and r=0.0564 (the decimal equivalent of 5.64%)


A=Pe%5E%28rt%29 Start with the continuous compounding formula.


1200=600%2Ae%5E%280.0564%2At%29 Plug in A=1200, P=600, and r=0.0564.


1200%2F600=e%5E%280.0564%2At%29 Divide both sides by 600.


2=e%5E%280.0564%2At%29 Evaluate 1200%2F600 to get 2.


ln%282%29=ln%28e%5E%280.0564%2At%29%29 Take the natural log of both sides.


ln%282%29=0.0564%2At%2Aln%28e%29 Pull down the exponent using the identity ln%28x%5Ey%29=y%2Aln%28x%29%29.


ln%282%29=0.0564%2At%2A1 Evaluate the natural log of 'e' to get 1.


ln%282%29=0.0564%2At Multiply and simplify.


0.693147180559945=0.0564%2At Evaluate the natural log of 2 to get 0.693147180559945 (this value is approximate).


0.693147180559945%2F0.0564=t Divide both sides by 0.0564 to isolate 't'.


12.2898436269494=t Evaluate 0.693147180559945%2F0.0564 to get 12.2898436269494.


t=12.2898436269494 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.