Pregunta
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A woman uses a loan program for small businesses to obtain a loan to help expand her vending machine business. The woman borrows \( \$ 29,000 \) for 4 years with a simple interest rate of \( 1.3 \% \). Determine the amount of money the woman must repay after 4 years. The woman must repay \( \$ \)

Ask by Sanders Bird. in the United States
Mar 09,2025

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The woman must repay \$30,508 after 4 years.

Solución

1. The formula for simple interest is given by: \[ I = P \times r \times t \] where: - \( P \) is the principal amount, - \( r \) is the annual interest rate (in decimal form), - \( t \) is the time in years. 2. Given: - \( P = 29000 \), - \( r = 1.3\% = 0.013 \), - \( t = 4 \) years. 3. Calculate the interest: \[ I = 29000 \times 0.013 \times 4 = 29000 \times 0.052 = 1508 \] So, the interest accrued over 4 years is \( \$1508 \). 4. The total amount to be repaid is the sum of the principal and the interest: \[ A = P + I = 29000 + 1508 = 30508 \] Thus, the woman must repay \( \$30508 \).

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The Deep Dive

To determine the total amount the woman must repay after 4 years, we'll first calculate the simple interest using the formula: \[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \] Here, the principal is \( \$29,000 \), the rate is \( 1.3\% = 0.013 \), and the time is 4 years. \[ \text{Interest} = 29,000 \times 0.013 \times 4 = 1,508 \] Now, to find the total amount to repay: \[ \text{Total Amount} = \text{Principal} + \text{Interest} = 29,000 + 1,508 = 30,508 \] Therefore, the amount the woman must repay after 4 years is \( \$30,508 \). --- In the world of small businesses, understanding loans is crucial! Many entrepreneurs utilize microloans or community financing programs to boost their ventures without hefty bank requirements. It's an empowering way to invest in one’s passions, like that vending machine business! Also, watch out for common pitfalls! Borrowers often forget to account for the full cost of borrowing, which includes interest and any potential fees. A clear understanding of the loan terms ensures businesses don’t end up overextended. Always read the fine print!

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