You are considering purchasing a new automobile that will cost you $28,000. The dealer offers you 4.9% APR (monthly compounding) financing for 60 months (with payments made at the end of the month). Assuming you finance the entire $28,000 and finance through the dealer, your monthly payments will be closest to:a.None of them.b.$457.c.$527.d.$1454.e.$467.
Question
You are considering purchasing a new automobile that will cost you 28,000 and finance through the dealer, your monthly payments will be closest to:a.None of them.b.527.d.467.
Solution
The correct answer is c. $527.
This is a loan payment problem where we know the loan amount (PV), the interest rate (r), and the number of periods (n), and we want to find out the monthly payment (PMT).
The formula for the monthly payment of a loan is:
PMT = PV * [r * (1 + r)^n] / [(1 + r)^n - 1]
Since the interest rate is given as an annual rate and the payments are monthly, we need to convert the interest rate to a monthly rate: r = 4.9% / 12 = 0.004083.
Substituting the given values into this formula gives:
PMT = $28,000 * [0.004083 * (1 + 0.004083)^60] / [(1 + 0.004083)^60 - 1]
Calculating this gives a monthly payment of approximately $527.
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