What is the approximate monthly P&I payment on a $350,000 loan at 4.75% for 30 years?

• A. Approximately $2,100 per month
• B. Approximately $1,500 per month
• C. Approximately $1,823 per month
• D. Approximately $2,500 per month

Answer: (C)

Fixed-rate mortgage payments are determined by the amortization formula: payment = P × i ÷ [1 − (1 + i)^(−n)], where P is the loan amount, i is the monthly interest rate, and n is the total number of payments.

Here, P = 350,000. The annual rate is 4.75%, so the monthly rate i = 0.0475 ÷ 12 ≈ 0.0039583. The term is 30 years, so n = 30 × 12 = 360.

Compute the factor (1 + i)^(−n) ≈ (1.0039583)^(−360) ≈ 0.241. Then the denominator becomes 1 − 0.241 ≈ 0.759. The numerator P × i ≈ 350,000 × 0.0039583 ≈ 1,385.42.

Divide: 1,385.42 ÷ 0.759 ≈ 1,827. This is essentially around $1,823 per month, which matches the given option.

So the approximate monthly principal and interest payment is about $1,823.