What is the standard mortgage payment formula and what do the variables represent?

What is the standard mortgage payment formula and what do the variables represent?

• A. Payment equals simple division of loan amount by number of payments.
• B. Payment equals fixed amount regardless of loan terms.
• C. Payment = P × [i(1+i)^n] / [(1+i)^n − 1], where P = loan amount, i = periodic interest rate, n = number of payments.
• D. Payment equals loan amount plus interest.

Answer: (C)

This tests understanding of the amortization formula used to set level loan payments that fully repay the loan over its term at a given periodic interest rate. The payment amount depends on three things: the loan amount (P), the periodic interest rate (i), and the total number of payments (n). The standard formula is P × [i(1+i)^n] / [(1+i)^n − 1], which comes from equating the present value of all equal payments to the loan amount. Here, i is the rate per payment period (for monthly payments, the annual rate divided by 12), and n is the total number of payments (years × 12 for monthly). This setup yields payments that cover both interest and principal so the loan is paid off after the final payment. Taxes and insurance are separate costs and not included in this formula. The other options don’t reflect how amortizing loans work: simply dividing the loan by the number of payments ignores interest, paying a fixed amount regardless of terms ignores how rate and term shape the payment, and adding interest to the loan amount isn’t how level amortizing payments are calculated.

This tests understanding of the amortization formula used to set level loan payments that fully repay the loan over its term at a given periodic interest rate. The payment amount depends on three things: the loan amount (P), the periodic interest rate (i), and the total number of payments (n). The standard formula is P × [i(1+i)^n] / [(1+i)^n − 1], which comes from equating the present value of all equal payments to the loan amount. Here, i is the rate per payment period (for monthly payments, the annual rate divided by 12), and n is the total number of payments (years × 12 for monthly). This setup yields payments that cover both interest and principal so the loan is paid off after the final payment. Taxes and insurance are separate costs and not included in this formula. The other options don’t reflect how amortizing loans work: simply dividing the loan by the number of payments ignores interest, paying a fixed amount regardless of terms ignores how rate and term shape the payment, and adding interest to the loan amount isn’t how level amortizing payments are calculated.