$$ \$ 1250 $$ are deposited in an account with a $$ 6.5 \% $$ interest rate, compounded continuously. What is the balance after 8 years? $$ F=\$[?] $$

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UpStudy AI · Accepted Answer

To find the balance after 8 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 $$ P = \$1250 $$
- Interest rate $$ r = 6.5\% = 0.065 $$
- Time $$ t = 8 $$ years

Substitute the values into the formula:

$$ F = 1250 \times e^{0.065 \times 8} $$

Now, we can calculate the final balance.
Calculate the value by following steps:
- step0: Calculate:
  $$1250e^{0.065\times 8}$$
- step1: Multiply the numbers:
  $$1250e^{0.52}$$
- step2: Convert the expressions:
  $$1250e^{\frac{13}{25}}$$
- step3: Rewrite the expression:
  $$1250\sqrt[25]{e^{13}}$$
The balance after 8 years with continuous compounding is approximately $2102.53.
The balance after 8 years is approximately \$2102.53.

are deposited in an account with a
interest rate, compounded
continuously.
What is the balance after 8 years?

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are deposited in an account with a interest rate, compounded continuously. What is the balance after 8 years?