QuestionJune 16, 2025

Antoine Smith wants a new pickup truck listed for 66,800 He will make a down payment of 30,000 and finance the balance at 9.87% interest for 6 years (72 months). Find the monthly payment using a calculator. Round your answer to the nearest cent. The monthly payment is Ssquare

Antoine Smith wants a new pickup truck listed for 66,800 He will make a down payment of 30,000 and finance the balance at 9.87% interest for 6 years (72 months). Find the monthly payment using a calculator. Round your answer to the nearest cent. The monthly payment is Ssquare
Antoine Smith wants a new pickup truck listed for 66,800 He will make a down payment of 30,000 and finance the balance at 9.87%  interest for
6 years (72 months). Find the monthly payment using a calculator. Round your answer to the nearest cent.
The monthly payment is Ssquare

Solution
4.5(231 votes)

Answer

S = 688.55 Explanation 1. Calculate the Loan Amount Subtract the down payment from the truck's price: 66,800 - 30,000 = 36,800. 2. Use the Loan Payment Formula The formula for monthly payment is **M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1}**, where P is the principal (36,800), r is the monthly interest rate, and n is the number of payments. 3. Convert Annual Interest Rate to Monthly Convert 9.87\% annual interest to a monthly rate: r = \frac{9.87}{100 \times 12} = 0.008225. 4. Calculate the Monthly Payment Substitute P = 36,800, r = 0.008225, and n = 72 into the formula: M = \frac{36,800 \cdot 0.008225 \cdot (1 + 0.008225)^{72}}{(1 + 0.008225)^{72} - 1}. 5. Compute Using Calculator Calculate the result using a calculator to find M.

Explanation

1. Calculate the Loan Amount<br /> Subtract the down payment from the truck's price: $66,800 - 30,000 = 36,800$.<br /><br />2. Use the Loan Payment Formula<br /> The formula for monthly payment is **$M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1}$**, where $P$ is the principal ($36,800$), $r$ is the monthly interest rate, and $n$ is the number of payments.<br /><br />3. Convert Annual Interest Rate to Monthly<br /> Convert $9.87\%$ annual interest to a monthly rate: $r = \frac{9.87}{100 \times 12} = 0.008225$.<br /><br />4. Calculate the Monthly Payment<br /> Substitute $P = 36,800$, $r = 0.008225$, and $n = 72$ into the formula:<br /> $M = \frac{36,800 \cdot 0.008225 \cdot (1 + 0.008225)^{72}}{(1 + 0.008225)^{72} - 1}$.<br /><br />5. Compute Using Calculator<br /> Calculate the result using a calculator to find $M$.
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