to purchase $12,300 worth of machinery for her business. rita made a down - payment of $1400 and took out a…
to purchase $12,300 worth of machinery for her business. rita made a down - payment of $1400 and took out a business loan for the rest, paying monthly payments of $483.10, she finally paid off the loan.\n(a) what was the total amount rita ended up paying for the machinery (including the down - payment and monthly payments)?\n$\n(b) how much interest did rita pay on the loan?\n$
Answer
Explanation:
Step1: Calculate the loan amount
The cost of machinery is $12300$ and the down - payment is $1400$. So the loan amount $L = 12300 - 1400=10900$.
Step2: Calculate the total amount of monthly payments
Assume the number of months is not given, but we know the monthly payment is $483.10$. Let's assume she paid for $n$ months until the loan was paid off. If we assume she paid off the loan in full with these monthly payments, we need to find the total of monthly payments. Let's assume she paid for $24$ months (since $10900\div483.10\approx22.56$, we assume a whole - number of months for simplicity. In a real - world scenario, we would need more information). The total of monthly payments $M = 483.10\times24 = 11594.4$.
Step3: Calculate the total amount paid for the machinery
The total amount $A$ paid for the machinery (including down - payment and monthly payments) is the sum of the down - payment and the total of monthly payments. So $A=1400 + 11594.4=12994.4$.
Step4: Calculate the interest paid on the loan
The interest $I$ paid on the loan is the total of monthly payments minus the loan amount. So $I = 11594.4-10900 = 694.4$.
Answer:
(a) $12994.4$ (b) $694.4$