Questions: Solve for the missing item in the following. Note: Do not round intermediate calculations. Round your answer to the nearest whole percent. Principal Interest rate Time Simple interest 5,400 % 19 months 342

Solve for the missing item in the following. Note: Do not round intermediate calculations. Round your answer to the nearest whole percent. Principal Interest rate Time Simple interest 5,400 % 19 months 342
Transcript text: Solve for the missing item in the following. Note: Do not round intermediate calculations. Round your answer to the nearest whole percent. \begin{tabular}{|c|c|c|c|c|c|} \hline \multicolumn{2}{|l|}{ Principal } & Interest rate & Time & \multicolumn{2}{|l|}{ Simple interest } \\ \hline \$ & 5,400 & \% & 19 months & \$ & 342 \\ \hline \end{tabular}
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Solution

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Solution Steps

To find the missing interest rate in a simple interest problem, we can use the formula for simple interest: \( I = P \times r \times t \), where \( I \) is the interest, \( P \) is the principal, \( r \) is the interest rate, and \( t \) is the time in years. We need to solve for \( r \). First, convert the time from months to years. Then, rearrange the formula to solve for \( r \) and calculate it using the given values.

Step 1: Identify the Known Values

We are given the principal amount \( P = 5400 \), the simple interest \( I = 342 \), and the time in months \( t = 19 \).

Step 2: Convert Time to Years

Since the time is given in months, we need to convert it to years. The conversion is done by dividing the number of months by 12: \[ t = \frac{19}{12} \approx 1.5833 \text{ years} \]

Step 3: Use the Simple Interest Formula

The formula for simple interest is: \[ I = P \times r \times t \] We need to solve for the interest rate \( r \). Rearranging the formula gives: \[ r = \frac{I}{P \times t} \]

Step 4: Calculate the Interest Rate

Substitute the known values into the formula: \[ r = \frac{342}{5400 \times 1.5833} \approx 0.0400 \] Convert the interest rate to a percentage by multiplying by 100: \[ r = 0.0400 \times 100 = 4.00\% \]

Final Answer

The interest rate is \(\boxed{4\%}\).

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