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DETAILS MY NOTES BRECMBC9 10.I.016.MI. ez Engineering borrows \( \$ 5,500 \), at \( 8 \frac{1}{2} \% \) interest, for 120 days. If the bank uses the ordinary interest method, how much interest (in \( \$ \) ) will the bank collect? (Round your answer to the nearest cent.) Help? Read it Watch it Master il

Ask by Lane Williams. in the United States
Feb 27,2025

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Answer

The bank will collect approximately \$155.83 in interest.

Solution

To calculate the interest using the ordinary interest method, use the formula:   Interest = Principal × Rate × Time where the time is given as a fraction of a 360-day year. Step 1: Convert the annual interest rate to a decimal.   8½% = 8.5% = 0.085 Step 2: Convert the loan period into years.   Time = 120 days ÷ 360 days/year = 120/360 = 1/3 year Step 3: Substitute the values into the formula.   Interest = 5500 × 0.085 × (1/3) Step 4: Calculate the value.   First, compute 5500 × 0.085 = 467.50   Then, 467.50 × (1/3) ≈ 155.83 Thus, the bank will collect approximately $155.83 in interest.

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To calculate the interest using the ordinary interest method, you can use the formula: \[ \text{Interest} = P \times r \times t \] where \( P \) is the principal amount (\$5,500), \( r \) is the interest rate (as a decimal), and \( t \) is the time in years. Since you're borrowing for 120 days, you'll convert that to years by dividing by 360 (ordinary interest method uses a 360-day year). First, convert the interest rate: \[ r = 8.5\% = 0.085 \] Then, convert the time: \[ t = \frac{120}{360} = \frac{1}{3} \] Now calculate the interest: \[ \text{Interest} = 5500 \times 0.085 \times \frac{1}{3} = 5500 \times 0.085 \times 0.3333 \approx 159.72 \] So, the bank will collect approximately \$159.72 in interest. Want to make your calculations even easier? Consider using a financial calculator or an online interest calculator! They can save you time and reduce the chance of mistakes, especially when you're dealing with different rates and time periods. Just input the values, and let the calculator do the work for you!

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