$$ \$ 3000 $$ are deposited in an account with $$ 9 \% $$ interest rate, compounded continuously. What is the balance after 14 years? $$ \mathrm{F}=\$[?] $$ Round to the nearest cent.

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To find the balance after 14 years with continuous compounding, we can use the formula for continuous compounding:

$$ A = P e^{rt} $$

Where:
- $$ A $$ is the amount after $$ t $$ years,
- $$ P $$ is the principal amount (initial deposit),
- $$ r $$ is the annual interest rate (in decimal form),
- $$ t $$ is the time in years.

Given:
- Principal amount $$ P = \$3000 $$,
- Annual interest rate $$ r = 9\% = 0.09 $$,
- Time $$ t = 14 $$ years.

Substitute the values into the formula:

$$ A = 3000 e^{0.09 \times 14} $$

Now, we can calculate the balance after 14 years.
Calculate the value by following steps:
- step0: Calculate:
  $$3000e^{0.09\times 14}$$
- step1: Multiply the numbers:
  $$3000e^{1.26}$$
- step2: Convert the expressions:
  $$3000e^{\frac{63}{50}}$$
The balance after 14 years with continuous compounding is approximately $10,576.26. Rounding to the nearest cent, the balance is $10,576.26.
The balance after 14 years is approximately \$10,576.26.

are deposited in an account with
interest rate, compounded
continuously.
What is the balance after 14 years?

Round to the nearest cent.

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are deposited in an account with interest rate, compounded continuously. What is the balance after 14 years? Round to the nearest cent.