Mullins Rose
07/22/2024 · Middle School

You deposit \( \$ 2000 \) in an account earning \( 6 \% \) interest compounded continuously. How much will you have in the account in 15 years?

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To calculate the amount in an account with continuous compounding interest, we 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 deposit), - \( r \) 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: - \( P = 2000 \) - \( r = 0.06 \) (which is \( 6\% \) expressed as a decimal) - \( t = 15 \) Now, we can substitute these values into the formula: \[ A = 2000 \cdot e^{0.06 \cdot 15} \] Calculating \( 0.06 \cdot 15 \): \[ 0.06 \cdot 15 = 0.9 \] Now, we can calculate \( e^{0.9} \): \[ e^{0.9} \approx 2.4596 \] Now, substituting this back into the formula: \[ A \approx 2000 \cdot 2.4596 \approx 4919.20 \] Thus, the amount in the account after 15 years will be approximately: \[ \boxed{4919.20} \]

Quick Answer

The amount in the account after 15 years will be approximately \$4919.20.
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