$$ \$ 900 $$ are deposited in an account with 70, interest rate, compounded continuously. What is the balance after 6 years? $$ F=\$[?] $$

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To find the balance after 6 years in an account with continuous compounding, we can use the formula for continuous compounding:

$$ F = P \times e^{rt} $$

Where:
- $$ F $$ is the final balance
- $$ P $$ is the principal amount (initial deposit)
- $$ r $$ is the interest rate
- $$ t $$ is the time in years

Given:
- Principal amount $$ P = \$900 $$
- Interest rate $$ r = 70\% = 0.70 $$
- Time $$ t = 6 $$ years

Substitute the given values into the formula:

$$ F = 900 \times e^{0.70 \times 6} $$

Now, we can calculate the final balance using the formula.
Calculate the value by following steps:
- step0: Calculate:
  $$900e^{0.7\times 6}$$
- step1: Multiply the numbers:
  $$900e^{4.2}$$
- step2: Convert the expressions:
  $$900e^{\frac{21}{5}}$$
The balance after 6 years in the account with continuous compounding is approximately $60017.70.
The balance after 6 years is approximately \$60,017.70.

are deposited in an account with 70,
interest rate, compounded continuously.
What is the balance after 6 years?

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