Pregunta
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ro purchase \( \$ 11.500 \) worth of restaurant equipment for her business, Amy made a down payment of \( \$ 1500 \) and took out a business loan for the rest. After years of paying monthly payments of \( \$ 304.23 \), she finally paid off the loan. (a) What was the total amount Amy ended up paying for the equipment (including the down payment and monthly payments)? \( \$ \square \) (b) How much interest did Amy pay on the loan?

Ask by Bowman Cruz. in the United States
Feb 28,2025

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(a) Amy paid a total of \$12,452.28 for the equipment. (b) She paid approximately \$952.28 in interest on the loan.

Solución

We start by noting that the equipment cost was US$11,500. Amy paid US$1,500 up‐front and financed the remaining   11,500 – 1,500 = US$10,000 with a business loan. Although the problem says “after years of paying monthly payments of US$304.23” it does not state the number of payments explicitly—in many textbook problems a three‑year (36‑month) term is assumed. (If the number of payments were different, the numerical answers below would change accordingly.) Assuming a 36‑month term, the total paid on the loan via monthly payments is   36 × 304.23 = US$10,952.28. (a) To find the total amount Amy ended up paying for the equipment, we add the down payment to the sum of the monthly payments:   Total paid = down payment + total monthly payments         = 1,500 + 10,952.28         ≈ US$12,452.28. (b) The interest paid on the loan is the extra amount over the original loan amount. Since the loan was for US$10,000, the interest is   Interest = total monthly payments – financed amount      = 10,952.28 – 10,000      ≈ US$952.28. Thus, under the assumption of a 36‑month repayment term: • (a) Amy paid approximately US$12,452.28 in total. • (b) Of that, about US$952.28 was interest. If the loan term were different from 36 months, you would simply compute the number of monthly payments (n) so that   Total paid on loan = 304.23 × n,   Total cost = 1,500 + (304.23 × n),   Interest = (304.23 × n) – 10,000. But with the common 36‑month assumption the answers above hold.

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The Deep Dive

To find the total amount Amy paid for the equipment, we need to sum up her down payment and total monthly payments. The first step is to determine how many months she paid her monthly payments. Let's say she took out a loan for \( x \) months. (a) The total amount paid for the equipment is calculated as: \[ \text{Total Payments} = \text{Down Payment} + \text{Monthly Payment} \times \text{Number of Months} \] \[ \text{Total Payments} = 1500 + 304.23 \times x \] Once we have the number of months \( x \), we can plug it into this formula to get the total amount. (b) To find out how much interest she paid, we can calculate the total cost of the loan (including interest) and subtract the principal amount borrowed. The amount borrowed is: \[ \text{Loan Amount} = \$ 11,500 - \$ 1,500 = \$ 10,000 \] The total interest paid is: \[ \text{Interest Paid} = \text{Total Payments} - \text{Loan Amount} \] To get the exact figures, we need the number of months \( x \) for the monthly payments. Exciting math, right? Go grab your calculator!

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