Question

what is the simple interest rate if $131.72 in interest is earned on a deposit of $1018.73 in one year? (i = prt)

the simple interest rate is \\(\square\\)%
(round to the nearest tenth as needed )

Explanation:

Step1: Recall the simple interest formula

The formula for simple interest is \( I = PRT \), where \( I \) is the interest, \( P \) is the principal amount, \( R \) is the interest rate (in decimal), and \( T \) is the time in years. We know \( I = 131.72 \), \( P = 1018.73 \), and \( T = 1 \) year. We need to solve for \( R \).

Step2: Rearrange the formula to solve for \( R \)

From \( I = PRT \), we can divide both sides by \( PT \) to get \( R=\frac{I}{PT} \).

Step3: Substitute the known values into the formula

Substitute \( I = 131.72 \), \( P = 1018.73 \), and \( T = 1 \) into the formula: \( R=\frac{131.72}{1018.73\times1} \).

Step4: Calculate the value of \( R \)

First, calculate the denominator: \( 1018.73\times1 = 1018.73 \). Then, divide \( 131.72 \) by \( 1018.73 \): \( R=\frac{131.72}{1018.73}\approx0.1293 \).

Step5: Convert \( R \) to a percentage

To convert the decimal to a percentage, multiply by 100: \( R\approx0.1293\times100 = 12.93\% \).

Step6: Round to the nearest tenth

Rounding \( 12.93\% \) to the nearest tenth gives \( 12.9\% \).

Answer:

\( 12.9 \)