Question
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
Real Tutor Solution
Tutor-Verified Answer
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
Reviewed and approved by the UpStudy tutoring team
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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, \( A = 4212 \).