16. Higher Order Thinking You have two different savings accounts. For Account A, the interest earned after 18 months is \( \$ 12.00 \). For Account B, the interest earned after 27 months is \( \$ 27.00 \). a. If the interest rate is \( 3.2 \% \) for Account \( A \), how much is the principal? b. If the interest rate is \( 2.4 \% \) for Account B, how much is the principal? c. Which account earned you the most interest in the first year? Explain.

To find the principal for Account A, use the formula for simple interest: \( I = P \times r \times t \). Rearranging, we find \( P = \frac{I}{r \times t} \). Plugging in the values for Account A, where \( I = 12 \), \( r = 0.032 \), and \( t = 1.5 \) (since 18 months = 1.5 years), we get \( P = \frac{12}{0.032 \times 1.5} \), which results in a principal of \( \$250 \). For Account B, using the same formula, where \( I = 27 \), \( r = 0.024 \), and \( t = 2.25 \) (27 months = 2.25 years), we have \( P = \frac{27}{0.024 \times 2.25} \). This results in a principal of approximately \( \$500 \). To determine which account earned the most interest in the first year, we calculate the interest from both accounts for a standard duration of one year. For Account A, using the principal of \( \$250 \), it earned \( 250 \times 0.032 \times 1 = \$8.00 \). For Account B, using the principal of \( \$500 \), it earned \( 500 \times 0.024 \times 1 = \$12.00 \). Thus, Account B earned more interest in the first year, illustrating how a lower interest rate can still yield better returns if based on a larger principal amount. So there you have it—a fun little financial detective adventure to uncover the best savings strategy!