SOLUTION: How much money, invested at an interest rate of r% per year compounded continuously, will amount to A dollars after t years? (Round your answer to the nearest cent.) A = 300,000,

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Question 741761: How much money, invested at an interest rate of r% per year compounded continuously, will amount to A dollars after t years? (Round your answer to the nearest cent.)
A = 300,000, r = 3.2, t = 14
I've gotten $191671.4 as the answer but it's counted wrong

Found 3 solutions by lynnlo, ikleyn, MathTherapy:
Answer by lynnlo(4176) About Me  (Show Source):
Answer by ikleyn(53419) About Me  (Show Source):
You can put this solution on YOUR website!
.
How much money, invested at an interest rate of r% per year compounded continuously,
will amount to A dollars after t years? (Round your answer to the nearest cent.)
A = 300,000, r = 3.2, t = 14
I've gotten $191671.4 as the answer but it's counted wrong
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Your equation is

    300000 = X%2Ae%5E%280.032%2A14%29,

where X is the principal under the problem's question.


From this equation, you find

    X = 300000%2Fe%5E%280.032%2A14%29 = 300000%2F2.7182818284%5E%280.032%2A14%29 = 191671.41 dollars (rounded to the nearest cent).


ANSWER. The principal amount is $191,671.41.

Solved.

The answer in the post by @lynnnlo is incorrect, so ignore it for the sake of the peace in your mind.



Answer by MathTherapy(10586) About Me  (Show Source):
You can put this solution on YOUR website!
How much money, invested at an interest rate of r% per year compounded continuously, will amount to A dollars after t years? (Round your answer to the nearest cent.)
A = 300,000,    r = 3.2,    t = 14

I've gotten $191671.4 as the answer but it's counted wrong

Approximate amount: $191,671.4052. 
Rounded to the NEAREST CENT results in $191,671.41, NOT $191,671.4 (presumed to be $191,671.40), as you stated.