Question
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An account earns annual simple interest. Find the interest earned, principal, interest rate, or time Interest earned: \( \$ 837 \), Principal: \( \$ 3100 \), Interest rate: ?, Time: 6 years.

Ask by Huff Bush. in the United States
Feb 19,2025

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Answer

The annual simple interest rate is 4.5%.

Solution

We use the simple interest formula:   Interest Earned (I) = Principal (P) × Rate (r) × Time (t) Given:   I = $837,   P = $3100,   t = 6 years. We need to find r. Step 1: Write the formula:   837 = 3100 × r × 6 Step 2: Solve for r by rearranging the formula:   r = 837 / (3100 × 6) Step 3: Calculate the denominator:   3100 × 6 = 18,600 Step 4: Divide to find r:   r = 837 / 18,600 = 0.045 Step 5: Convert to a percentage:   0.045 × 100 = 4.5% Thus, the annual simple interest rate is 4.5%.

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The Deep Dive

To find the interest rate in this scenario, you can use the simple interest formula: \( \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \). Rearranging the formula gives you \( \text{Rate} = \frac{\text{Interest}}{\text{Principal} \times \text{Time}} \). Plugging in your numbers, that’s \( \frac{837}{3100 \times 6} \), which will help you work out the rate. Now, when calculating simple interest, don’t forget that the interest accrued is always based on the principal—it doesn’t compound! This means that for each year, the interest remains constant and is calculated solely off the initial amount of money put in. Doing the math step-by-step ensures you won’t miss anything and won’t end up confused!

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