What is the formula to calculate the monthly payment (PMT) on a 60-month loan with principal \(P\), annual interest rate \(r\), and monthly payments?

• A. PMT = \frac{P}{60}
• B. PMT = P \times (1 + r)^{60}
• C. PMT = P \times r \times 60
• D. PMT = \frac{P \times r}{1 - (1 + r)^{-60}}

Answer: (D)

Verified step by step guidance

1. Understand the problem: The goal is to calculate the monthly payment (PMT) for a loan using the correct formula. The formula provided is PMT = \frac{P \times r}{1 - (1 + r)^{-60}}, where P is the loan principal, r is the monthly interest rate, and the loan term is 60 months.
2. Step 1: Convert the annual interest rate to a monthly interest rate. If the annual interest rate is given as a percentage, divide it by 12 and convert it to a decimal. For example, if the annual interest rate is 6%, the monthly interest rate r = \frac{6}{100 \times 12}.
3. Step 2: Calculate the denominator of the formula. The denominator is 1 - (1 + r)^{-60}. First, add 1 to the monthly interest rate r, then raise the result to the power of -60 (negative exponent). Finally, subtract this value from 1.
4. Step 3: Calculate the numerator of the formula. The numerator is P \times r, where P is the loan principal and r is the monthly interest rate. Multiply these two values together.
5. Step 4: Divide the numerator by the denominator to find the monthly payment (PMT). Use the formula PMT = \frac{P \times r}{1 - (1 + r)^{-60}} to complete the calculation.