SOLUTION: Please help me 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 intere

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Question 145702: Please help me 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.
Use the formula given to solve the following:
a) Maya has deposited $600 in an account that pays 5.64% interest, compounded continuously. How long will it take for her money to double?
b) Suppose that $2000 is invested at a rate of 6% per year compounded continuously. What is the balance after 1 yr? After 2 yrs?
Please help me figure this problem out.
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
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.
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Use the formula given to solve the following:
a) Maya has deposited $600 in an account that pays 5.64% interest, compounded continuously. How long will it take for her money to double?
2*600 = 600e^(0.0564t)
2 = e^(0.0564t)
Take the natural log of both sides to get:
0.0564t = ln2
t = ln2/0.0564
t = 12.2898..years
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b) Suppose that $2000 is invested at a rate of 6% per year compounded continuously. What is the balance after 1 yr? After 2 yrs?
A(1) = 2000e^(0.06*1) = $2123.67
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A(2) = 2000e^(0.06*2) = $2254.99
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Cheers,
Stan H.
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Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a)

A=Pe%5E%28rt%29 Start with the given formula


1200=600e%5E%280.0564t%29 Plug in P=600, A=1200 (which is double her investment), and r=0.0564


2=e%5E%280.0564t%29 Divide both sides by 600


ln%282%29=0.0564t Take the natural log of both sides


0.69315=0.0564t Take the natural log of 2 to get 0.69315


12.28989=t Divide both sides by 0.0564


So the answer is t=12.28989. So it takes a little over 12 years to double her money.




b)

A=Pe%5E%28rt%29 Start with the given formula


A=2000e%5E%280.06t%29 Plug in P=2000 and r=0.06


"What is the balance after 1 yr?"

A=2000e%5E%280.06%2A1%29 Plug in t=1


A=2000e%5E%280.06%29 Multiply


A=2000%281.06183%29 Raise e to the 0.06 power to get 1.06184


A=2123.66 Multiply


So after 1 year, the balance is $2,123.66


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"What is the balance after 2 yrs?"

A=2000e%5E%280.06%2A2%29 Plug in t=2


A=2000e%5E%280.12%29 Multiply


A=2000%281.1275%29 Raise e to the 0.12 power to get 1.1275


A=2255 Multiply


So after 2 years, the balance is $2,255