To calculate the amount in an account with continuous compounding, 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 investment),
- \( r \) is the annual interest rate (as a 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:
- \( P = 1600 \)
- \( r = 4.6% = 0.046 \)
- \( t = 4 \)
Now, plug the values into the formula:
\[ A = 1600 \cdot e^{(0.046 \cdot 4)} \]
Calculate \( 0.046 \cdot 4 \):
\[ 0.046 \cdot 4 = 0.184 \]
Now calculate \( e^{0.184} \):
Using a calculator or exponentiation function:
\[ e^{0.184} \approx 1.2027 \]
Now, substitute this back into the equation for \( A \):
\[ A \approx 1600 \cdot 1.2027 \approx 1924.32 \]
Therefore, after 4 years, you will have approximately $1924.32 in the account.
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