How is the monthly mortgage rate derived from the annual rate?

• A. Monthly rate = (1 + Annual rate)^(1/12) - 1
• B. Monthly rate = Annual rate / 12
• C. Monthly rate = Annual rate * 12
• D. Monthly rate = Annual rate / 365

Answer: (B)

Dividing the annual rate by 12 is the standard way to get the monthly rate for a mortgage because payments occur monthly and lenders quote interest as a nominal annual rate that is split evenly across the 12 months. The monthly rate i is r/12, so a 6% annual rate becomes 0.06/12 = 0.005, or 0.5% per month. That monthly rate is what you plug into the amortization formula to compute each fixed payment: Payment = Loan × [i(1+i)^n] / [(1+i)^n − 1], where n is the number of payments. This approach reflects how most mortgage quotes are structured, dividing the yearly rate into equal monthly portions. Using the twelfth root of (1+r) minus 1 would correspond to converting an effective annual rate to a monthly rate, which isn’t the standard method for nominal APR mortgage quotes. Dividing by 12 aligns with monthly compounding assumptions, while multiplying by 12 or dividing by 365 doesn’t match how monthly payments are calculated.