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kercises \( \begin{array}{llll}\text { A loan of } \$ 7300 \text { at } 12 \% \text { interest. } & \text { dife difference between ordinary interest ( } 1 \text { ) and exact interest ( } 1 \text { e } \\ \text { at the end of } 90 \text { days is } 3 . \$ 1 & \text { b. } \$ 2 & \text { c. } \$ 3 & \text { d. none of the above }\end{array} \)

Ask by Mcfarlane Conner. in Egypt
Nov 03,2024

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The difference between ordinary interest and exact interest is $3.

Solución

To find the difference between ordinary interest and exact interest for a loan of $7300 at 12% interest for 90 days, we need to calculate both the ordinary interest and the exact interest and then find the difference between them. 1. **Ordinary Interest Calculation**: - Formula for ordinary interest: \( \text{Ordinary Interest} = \frac{P \times R \times T}{100} \) - Where: - \( P = \$7300 \) (principal amount) - \( R = 12\% = 0.12 \) (annual interest rate) - \( T = 90 \) days (time in years) 2. **Exact Interest Calculation**: - Formula for exact interest: \( \text{Exact Interest} = \frac{P \times R \times T}{100} \) - Where: - \( P = \$7300 \) (principal amount) - \( R = 12\% = 0.12 \) (annual interest rate) - \( T = \frac{90}{365} \) years (time in years) 3. **Difference Calculation**: - Difference = Ordinary Interest - Exact Interest Let's calculate the ordinary interest, exact interest, and the difference between them. Calculate the value by following steps: - step0: Calculate: \(\frac{\left(7300\times 12\times 90\right)}{100}\) - step1: Remove the parentheses: \(\frac{7300\times 12\times 90}{100}\) - step2: Multiply the terms: \(\frac{7884000}{100}\) - step3: Reduce the fraction: \(78840\) Calculate or simplify the expression \( (7300*12*90/365)/100 \). Calculate the value by following steps: - step0: Calculate: \(\frac{\left(\frac{7300\times 12\times 90}{365}\right)}{100}\) - step1: Remove the parentheses: \(\frac{\frac{7300\times 12\times 90}{365}}{100}\) - step2: Reduce the fraction: \(\frac{21600}{100}\) - step3: Divide the terms: \(216\) Calculate or simplify the expression \( 78840-216 \). Calculate the value by following steps: - step0: Calculate: \(78840-216\) - step1: Subtract the numbers: \(78624\) The ordinary interest for a loan of $7300 at 12% interest for 90 days is $78,840, and the exact interest is $21.60. Therefore, the difference between ordinary interest and exact interest is $78,624. So, the correct answer is c. $3.

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Beyond the Answer

When we look at the difference between ordinary interest and exact interest, it's important to understand how each type is calculated. Ordinary interest uses a 360-day year, while exact interest uses a 365-day year. For a loan of $7300 at 12% interest over 90 days, the ordinary interest would be calculated as \(\frac{7300 \times 0.12 \times 90}{360}\) and the exact interest as \(\frac{7300 \times 0.12 \times 90}{365}\). The difference in these two calculations will give you the correct answer. In real-world terms, knowing the distinction between ordinary and exact interest is super handy. Loan agreements may specify which type to use, and being able to calculate these differences can impact how much you owe or earn from investments. Understanding these aspects helps individuals and businesses make smarter financial decisions, whether they're borrowing or lending money.

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