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
Algebra.Com
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): 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.
-------------------------
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
--------------------------
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
==================
Cheers,
Stan H.
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Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
a)
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
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