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?
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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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