To calculate the amount in the account after 4 years with continuous compounding interest, 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 (decimal),
- \( t \) is the time the money is invested for (in years),
- \( e \) is the base of the natural logarithm (approximately equal to 2.71828).
Given:
- \( P = 8000 \) (the initial amount),
- \( r = 0.07 \) (7% interest),
- \( t = 4 \) (4 years).
Substituting the values into the formula, we get:
\[ A = 8000 \times e^{0.07 \times 4} \]
Calculating \( 0.07 \times 4 \):
\[ 0.07 \times 4 = 0.28 \]
Now, we calculate \( e^{0.28} \):
\[ e^{0.28} \approx 1.32313 \]
Now substitute back into the formula:
\[ A \approx 8000 \times 1.32313 \]
Calculating \( 8000 \times 1.32313 \):
\[ A \approx 10585.04 \]
Rounding to the nearest cent:
\[ A \approx 10585.04 \]
Therefore, the amount in the account after 4 years will be $10,585.04.
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