Questions: Find the simple interest. Then use the compound interest table to find the interest compounded annually. Finally, find the amount by which the compound interest is larger than the simple interest. What is the simple interest? 8 (Round to the nearest cent as needed.)

Find the simple interest. Then use the compound interest table to find the interest compounded annually. Finally, find the amount by which the compound interest is larger than the simple interest. What is the simple interest? 8 (Round to the nearest cent as needed.)
Transcript text: Find the simple interest. Then use the compound interest table to find the interest compounded annually. Finally, find the amount by which the compound interest is larger than the simple interest. What is the simple interest? 8 $\square$ (Round to the nearest cent as needed.)
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Solution

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Solution Steps

Step 1: Calculate Simple Interest (SI)

Using the formula \(SI = \frac{P \times R \times T}{100}\), where \(P = 5300\), \(R = 10\%\), and \(T = 4\) years, we calculate the simple interest as \(SI = \frac{5300 \times 10 \times 4}{100} = 2120\).

Step 2: Calculate Compound Interest (CI)

Using the formula \(CI = P \times (1 + \frac{R}{100})^T - P\), where \(P = 5300\), \(R = 10\%\), and \(T = 4\) years, we calculate the compound interest as \(CI = 5300 \times (1 + \frac{10}{100})^{4} - 5300 = 2459.73\).

Step 3: Find the Difference

The difference between the compound interest and the simple interest is calculated as \(Difference = CI - SI = 339.73\).

Final Answer:

The simple interest is 2120, the compound interest is 2459.73, and the difference is 339.73.

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