B. To find the loan period \( t \), solve \( I=\operatorname{Prt} \) for \( t \). (3) \[ \begin{aligned} I=P \times r \times t & =7,500 \times \\ & =450 \times t \\ & =t \end{aligned} \] The loan period was \( \qquad \) years.
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The Deep Dive
To solve for \( t \) in the equation \( I = Prt \), you need to rearrange the formula to isolate \( t \). This means you divide both sides by \( Pr \): \[ t = \frac{I}{Pr} \] In this scenario, if you plug in the numbers with \( I = 450 \), \( P = 7500 \), and \( r = 0.06 \) (assuming 6% as the interest rate), you can calculate \( t \) and find that the loan period is \( 1 \) year. In real-world scenarios, understanding the loan period is crucial in making informed financial decisions. Shorter loan periods often mean higher monthly payments but less interest paid overall, while longer periods can ease monthly expenses but result in more interest paid over time. So be strategic when choosing your loan term!