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Question 1033122: Suppose you deposit $275 in an account paying 4% annual interest, compounded continuously. Approximately how many years will it take for you to have $394 in your account?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you deposit 275 paying 4% annual interest compounded continuously.
how many years to have 394.
the continuous compounding formula is f = p * e^(rn)
f is the future value
p is the present value
r is the interest rate per time period.
n is the number of time periods.
you are given the annual interest rate.
the time period is therefore in years.
the formula becomes f = p * e^(.04*n)
since f = 394 and p = 275, the formula becomes 394 = 275 * e^(.04*n)
divide both sides of this formula by 275 to get:
394/275 = e^(.04*n)
take the natural log of both sides of this equation to get ln(394/275) = ln(e^(.04*n)).
since ln(e^(.04*n)) is equivalent to .04*n*ln(e), the formula becomes ln(394/275) = .04*n*ln(e).
since ln(e) = 1, the formula becomes ln(394/275) = .04*n
divide both sides of this equation by .04 to get ln(394/275)/.04 = n
solve for n to get n = ln(394/275)/.04 = 8.989495291.
to confirm this is correct, replace n in your original equation to get 294 = 275 * e^(.04*8.989495291).
you will get 394 = 394.
this confirms the solution is correct.
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