Question
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In order to start a small business; a student takes out a simple interest loan for \( \$ 3000 \) for 3 months at a rate of \( 8.75 \% \). a. How much interest must the student pay? b. Find the future value of the loan. a. The amount of interest is \( \$ 65.63 \). (Round to the nearest cent as needed.) b. The future value of the loan is \( \$ 3065.63 \). (Round to the nearest cent as needed.)

Ask by Gibson Mills. in the United States
Feb 25,2025

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Answer

a. The student must pay $65.63 in interest. b. The future value of the loan is $3065.63.

Solution

To find the interest for a simple interest loan, use the formula:   Interest = Principal × Rate × Time Here:   Principal (P) = $3000   Annual Interest Rate (r) = 8.75% = 0.0875   Time (t) = 3 months = 3/12 years = 0.25 years a. Calculate Interest:   Interest = 3000 × 0.0875 × 0.25   Interest = 3000 × 0.021875   Interest = $65.625 Rounded to the nearest cent, the interest is $65.63. b. The future value of the loan is the sum of the principal and the interest:   Future Value = Principal + Interest   Future Value = $3000 + $65.63   Future Value = $3065.63 Thus, the answers are:   a. Interest = $65.63   b. Future Value = $3065.63

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Bonus Knowledge

Did you know that simple interest has been a go-to method for lenders since ancient times? The concept can be traced back to the Babylonians in 2000 BC, who utilized basic formulas to calculate interest on borrowed goods, making it easier for individuals to manage debts and investments. Fast forward a few millennia, and you're facing a financial landscape where understanding concepts like simple interest is crucial for small business success! On the practical side, many first-time borrowers trip up by not fully understanding the terms of their loans. Always check if the interest rate is fixed or variable and the duration before signing the dotted line. Mistakes like overlooking additional fees can lead to unexpected costs, turning a manageable loan into a financial burden. Understanding these details can empower you and help keep your business finances in check!

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