To find the amount in a continuously compounded account, you can use the formula:
\[ A = Pe^{rt} \]
where:
- \( A \) is the amount of money accumulated after time \( t \).
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (in decimal).
- \( t \) is the time the money is invested or borrowed for, in years.
- \( e \) is the base of the natural logarithm, approximately equal to 2.71828.
Given:
- \( P = 5000 \)
- \( r = 5.6% = 0.056 \)
- \( t = 3 \)
Plugging in the values:
\[ A = 5000 \times e^{(0.056 \times 3)} \]
Calculating the exponent:
\[ 0.056 \times 3 = 0.168 \]
Now, calculating \( e^{0.168} \):
\[ e^{0.168} \approx 1.18380 \] (rounded to five decimal places)
Now, we can calculate \( A \):
\[ A = 5000 \times 1.18380 \]
\[ A \approx 5919.00 \]
Therefore, the balance after 3 years is approximately:
\[ \boxed{5919.00} \]
(rounded to the nearest cent).
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