Question
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Where, \( A \) is the amount \( P \) is the principal \( r \) is the annual simple interest rate (written as a decimal) \( t \) is the time in years. \( P=\$ 3,900 ; r=8 \% ; t=1 \) year; \( A= \) ? \( A=\$ \square \) (Type an integer or a decimal.)

Ask by Hamilton Hills. in the United States
Jan 22,2025

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Answer

\( A = \$4,212 \)

Solution

To calculate the amount \( A \) using the simple interest formula: \[ A = P(1 + rt) \] Given: - \( P = \$3,900 \) - \( r = 8\% = 0.08 \) - \( t = 1 \) year Plugging in the values: \[ A = 3900 \times (1 + 0.08 \times 1) = 3900 \times 1.08 = 4212 \] \[ A = \$4,212 \] **Answer:** \$4212

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Extra Insights

To calculate the total amount \( A \) using the simple interest formula \( A = P + (P \cdot r \cdot t) \), you first need to compute the interest earned. Given \( P = 3900 \), \( r = 0.08 \) (which is 8% expressed as a decimal), and \( t = 1 \), you find the interest: \[ \text{Interest} = P \cdot r \cdot t = 3900 \cdot 0.08 \cdot 1 = 312 \] Now, add the interest back to the principal to find the amount \( A \): \[ A = P + \text{Interest} = 3900 + 312 = 4212 \] Thus, \( A = 4212 \).

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