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

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.

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

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: $$t = \frac{19}{12} \approx 1.5833 \text{ years}$$

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: $$r = \frac{I}{P \times t}$$

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