$$ \$ 900 $$ are deposited in an account with $$ 4 \% $$ interest rate, compounded continuously. What is the balance after 10 years? $$ F=\$[?] $$

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UpStudy AI · Accepted Answer

To find the balance after 10 years 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 $$ r = 4\% = 0.04 $$
- Time $$ t = 10 $$ years

Substitute the values into the formula:

$$ F = 900 \times e^{0.04 \times 10} $$

Now, we can calculate the final balance.
Calculate the value by following steps:
- step0: Calculate:
  $$900e^{0.04\times 10}$$
- step1: Multiply the numbers:
  $$900e^{0.4}$$
- step2: Convert the expressions:
  $$900e^{\frac{2}{5}}$$
- step3: Rewrite the expression:
  $$900\sqrt[5]{e^{2}}$$
The balance after 10 years with continuous compounding is approximately $1342.64.
The balance after 10 years is approximately \$1,342.64.

are deposited in an account with
interest rate, compounded continuously.
What is the balance after 10 years?

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are deposited in an account with interest rate, compounded continuously. What is the balance after 10 years?