Question

what is the simple interest rate if $ 51.52 in interest is earned on a deposit of $1095.79 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, and \( T \) is the time in years. We know \( I = 51.52 \), \( P = 1095.79 \), and \( T = 1 \) (since it's one 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 \( I = 51.52 \), \( P = 1095.79 \), and \( T = 1 \) into the formula: \( R=\frac{51.52}{1095.79\times1} \).

Step4: Calculate the value of R

First, calculate the denominator: \( 1095.79\times1 = 1095.79 \). Then, divide \( 51.52 \) by \( 1095.79 \): \( R=\frac{51.52}{1095.79}\approx0.04702 \).

Step5: Convert R to a percentage

To convert a decimal to a percentage, multiply by 100: \( R\approx0.04702\times100 = 4.702\% \).

Step6: Round to the nearest tenth

Rounding \( 4.702\% \) to the nearest tenth gives \( 4.7\% \).

Answer:

\( 4.7 \)