SOLUTION: Suppose $50,000 was deposited in the bank with an interest rate of 5.5% annually, compounded continuously. A) How long will it take to double the original amount? B) Find the bal

Question 412133: Suppose $50,000 was deposited in the bank with an interest rate of 5.5% annually, compounded continuously.
A) How long will it take to double the original amount?
B) Find the balance after 30 years.
C) Determine how many years it will take for the amount to be %1,000,000.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Suppose $50,000 was deposited in the bank with an interest rate of 5.5% annually, compounded continuously.
A(t) = Pe^(rt)
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A) How long will it take to double the original amount?
2P = P*e^(rt)
e^(rt) = 2
e^(0.055t) = 2
0.055t = ln(2)
t = [ln(2)]/0.055
t = 12.6 years
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B) Find the balance after 30 years.
Solve A(30) = 50,000*e^(0.055*30)
A(30) = $260,348.99
-----------------------------
C) Determine how many years it will take for the amount to be %1,000,000.
--------
Solve 1,000,000 = 50,000e^(0.055t)
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Cheers,
Stan H.
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