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At the City National Credit Union, a \( 8 \%, \$ 7,000 \) loan for 190 days had interest charges of \( \$ 291.51 \). What type of interest did City National use, ordinary or exact ordinary exact SUBMIT ANSWER

Ask by Mathis Pierce. in the United States
Feb 26,2025

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Answer

City National used the exact interest method.

Solution

To determine which method was used, we compare the interest that would be charged under the two common methods: 1. Ordinary interest (using a 360‐day year):   Interest = Principal × Rate × (Days/360)   = 7000 × 0.08 × (190/360)   = 7000 × 0.08 × 0.52778 (approximately)   ≈ 7000 × 0.04222   ≈ 295.11 2. Exact interest (using a 365‐day year):   Interest = Principal × Rate × (Days/365)   = 7000 × 0.08 × (190/365)   = 7000 × 0.08 × 0.52055 (approximately)   ≈ 7000 × 0.041644   ≈ 291.51 Since the given interest charge is $291.51, the calculation corresponds to the exact interest method. Answer: exact.

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City National Credit Union likely used ordinary interest for their calculations. This method considers a 360-day year when calculating interest, which typically yields a higher amount of interest than the exact method that uses a 365-day year. Given the interest charged for a relatively short loan duration of 190 days, ordinary interest is commonly preferred by institutions due to the favorable interest summation it provides. Using the formula for ordinary interest, \( I = P \times r \times t \), where \( P \) is the principal, \( r \) is the rate, and \( t \) is time in years (calculated as days/360), you can verify the interest. If we plug in the numbers, it confirms the type of interest used. It's a neat way to crunch the numbers and understand why certain institutions favor one method over another!

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