To determine which equation represents the total value of an investment with simple interest, we need to understand the formula for calculating simple interest. The formula for the total value, \( V \), of an investment with simple interest is:
[tex]\[ V = P + (P \cdot r \cdot t) \][/tex]
Where:
- \( P \) is the principal amount (the initial amount invested),
- \( r \) is the annual interest rate (expressed as a decimal),
- \( t \) is the time the money is invested for (in years).
Given:
- The principal amount, \( P \), is \$12,000.
- The annual interest rate, \( r \), is \(7.15\%\) or \(0.0715\) as a decimal.
Let's substitute these values into our formula:
[tex]\[ V = 12,000 + (12,000 \cdot 0.0715 \cdot t) \][/tex]
Simplify the expression inside the parentheses:
[tex]\[ V = 12,000 + 12,000(0.0715)t \][/tex]
This corresponds to option B. Therefore, the equation that represents the total value of Ava’s investment after \( t \) years is:
[tex]\[ V = 12,000 + 12,000(0.0715)t \][/tex]
Hence, the correct answer is B.
