Which formula represents the standard fixed-rate mortgage monthly payment (P&I) given the loan amount, monthly rate, and total payments?

Which formula represents the standard fixed-rate mortgage monthly payment (P&I) given the loan amount, monthly rate, and total payments?

• A. P&I = PV * r * (1+r)^n
• B. P&I = [r*PV]/[1 - (1+r)^-n]
• C. P&I = PV / [1 - (1+r)^-n] * r
• D. P&I = PV * [1 - (1+r)^-n] / r

Answer: (B)

The payments for a fixed-rate mortgage are set so the loan is fully paid off after the term by balancing interest and principal in each monthly payment. With the loan amount PV, the monthly rate r, and total number of payments n, the level monthly payment is P = (r * PV) / [1 - (1 + r)^-n]. The numerator r * PV represents the amount needed to cover the interest on the current balance each month, while the denominator [1 - (1 + r)^-n] accounts for spreading those payments over the full term so the balance goes to zero at the end. This form is the standard way to express the fixed payment in amortization schedules and mortgage calculators. The other options either omit the necessary division by the amortization factor or arrange the terms in a way that wouldn’t produce the correct level payment.

The payments for a fixed-rate mortgage are set so the loan is fully paid off after the term by balancing interest and principal in each monthly payment. With the loan amount PV, the monthly rate r, and total number of payments n, the level monthly payment is P = (r * PV) / [1 - (1 + r)^-n]. The numerator r * PV represents the amount needed to cover the interest on the current balance each month, while the denominator [1 - (1 + r)^-n] accounts for spreading those payments over the full term so the balance goes to zero at the end. This form is the standard way to express the fixed payment in amortization schedules and mortgage calculators. The other options either omit the necessary division by the amortization factor or arrange the terms in a way that wouldn’t produce the correct level payment.