Connor invested $$ \$ 59,000 $$ in an account paying an interest rate of $$ 2.6 \% $$ compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 12 years?

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To find the amount of money in the account after 12 years, we can use the formula for continuous compounding:

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

Where:
- $$ A $$ is the amount of money in the account after $$ t $$ years,
- $$ P $$ is the principal amount (initial investment),
- $$ r $$ is the interest rate,
- $$ t $$ is the time in years.

Given:
- $$ P = \$59,000 $$
- $$ r = 2.6\% = 0.026 $$
- $$ t = 12 $$ years

Substitute the values into the formula:

$$ A = 59000 \times e^{0.026 \times 12} $$

Now, we can calculate the amount of money in the account after 12 years.
Calculate the value by following steps:
- step0: Calculate:
  $$59000e^{0.026\times 12}$$
- step1: Multiply the numbers:
  $$59000e^{0.312}$$
- step2: Convert the expressions:
  $$59000e^{\frac{39}{125}}$$
- step3: Rewrite the expression:
  $$59000\sqrt[125]{e^{39}}$$
The amount of money in the account after 12 years is approximately $80,603.13.

Rounded to the nearest hundred dollars, the amount of money in the account after 12 years is $80,600.
After 12 years, Connor will have approximately \$80,600 in the account.

Connor invested in an account paying an interest rate of compounded
continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest
hundred dollars, would be in the account after 12 years?

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Connor invested in an account paying an interest rate of compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 12 years?