

Click here to see ALL problems on logarithm 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) (Show Source):

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?

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

---------

A(2) = 2000e^(0.06*2) = $2254.99

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Cheers,

Stan H.

---------------- You can put this solution on YOUR website!

Answer by jim_thompson5910(35256) (Show Source):





Start with the given formula





Plug in , (which is double her investment), and





Divide both sides by 600





Take the natural log of both sides





Take the natural log of 2 to get 0.69315





Divide both sides by 0.0564





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









b)



Start with the given formula





Plug in and





"What is the balance after 1 yr?"



Plug in





Multiply





Raise e to the 0.06 power to get 1.06184





Multiply





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





---------------------





"What is the balance after 2 yrs?"



Plug in





Multiply





Raise e to the 0.12 power to get 1.1275





Multiply





So after 2 years, the balance is $2,255 a)Start with the given formulaPlug in(which is double her investment), andDivide both sides by 600Take the natural log of both sidesTake the natural log of 2 to get 0.69315Divide both sides by 0.0564So the answer is. So it takes a little over 12 years to double her money.b)Start with the given formulaPlug inand"What is the balance after 1 yr?"Plug inMultiplyRaise e to the 0.06 power to get 1.06184MultiplySo after 1 year, the balance is $2,123.66---------------------"What is the balance after 2 yrs?"Plug inMultiplyRaise e to the 0.12 power to get 1.1275MultiplySo after 2 years, the balance is $2,255 You can put this solution on YOUR website!

