To calculate the future value of an annuity where the first deposit is made today (also known as an annuity due), we can use the formula for the future value of an annuity due:
\[ FV = P \times \left( (1 + r)^n - 1 \right) \times (1 + r) / r \]
Where:
- \( FV \) is the future value of the annuity
- \( P \) is the annual payment ($2,073.00)
- \( r \) is the annual interest rate (7.00% or 0.07)
- \( n \) is the total number of deposits (5)
First, we'll plug in the values.
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Calculate \( (1 + r) \): \[ 1 + r = 1 + 0.07 = 1.07 \]
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Calculate \( (1 + r)^n \): \[ (1.07)^5 = 1.402552 \]
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Now calculate the future value using the above result: \[ FV = 2073 \times \left( 1.402552 - 1 \right) \times \frac{1.07}{0.07} \]
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Calculate \( 1.402552 - 1 \): \[ 1.402552 - 1 = 0.402552 \]
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Now calculate \( \frac{1.07}{0.07} \): \[ \frac{1.07}{0.07} = 15.28571429 \]
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Substitute back into the formula: \[ FV = 2073 \times 0.402552 \times 15.28571429 \]
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Now perform the operations: \[ 2073 \times 0.402552 \approx 834.897 \] \[ FV \approx 834.897 \times 15.28571429 \approx 12,762.547 \]
Thus, the amount in the account 5.0 years from today will be approximately:
\[ \boxed{12,762.55} \]
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