Pregunta
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purchase \( \$ 13,500 \) worth of machinery for her business, Christine made a down payment of \( \$ 1500 \) and took out isiness loan for the rest. After 3 years of paying monthly payments of \( \$ 365.07 \), she finally paid off the loan. \( \begin{array}{l}\text { (a) What cost and interest for a loan } \\ \text { (including the down payment and monthly payments)? } \\ \text { (b) How much interest did Christine pay on the loan? } \\ \$ \square\end{array} \$ \square \)

Ask by Ramos Hall. in the United States
Mar 18,2025

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The total cost of the loan is \$14,642.52, and Christine paid \$2,642.52 in interest.

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The Deep Dive

To calculate the total cost and interest for the loan Christine took out for the machinery, we first need to find out how much she borrowed. The cost of the machinery was \( \$ 13,500 \), and after making a down payment of \( \$ 1,500 \), the amount she financed with a loan was \( \$ 13,500 - \$ 1,500 = \$ 12,000 \). Now, Christine paid \( \$ 365.07 \) monthly for 3 years, which amounts to \( 3 \times 12 \) months, resulting in 36 monthly payments. Multiplying the monthly payment by the total number of payments gives us: \[ \$ 365.07 \times 36 = \$ 13,141.52 \] This total represents all the payments made on the loan. To find the total cost, we add the down payment: \[ \text{Total Cost} = \$ 13,141.52 + \$ 1,500 = \$ 14,641.52 \] Next, to determine how much interest Christine paid on the loan, we calculate the difference between the total amount paid for the loan and the original loan amount: \[ \text{Total Interest} = \$ 13,141.52 - \$ 12,000 = \$ 1,141.52 \] So, to summarize: (a) Total cost including down payment and monthly payments: \( \$ 14,641.52 \) (b) Total interest paid on the loan: \( \$ 1,141.52 \)

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