# How Do You Calculate Mortgage Payments

Q: I'm interested in knowing exactly how it is that mortgages are calculated. The internet is no help because all search attempts point to mortgage calculators, not the method of mortgage calculating. Any explanation or comments for me???

A: If the interest is compounded monthly, the mortgage payment can be computed by: PMT = PV * r / (1 - 1/((1 + r)^n)) where PV is the loan amount, n is the length of the loan in months, and r is i/12, where i is the nominal annual interest rate (not the APR). In Excel, it is simply PMT(i/12, n,, -PV). The lender should always round __up__ PMT at least to cents to ensure that the last payment is no more than the others -- unless the lender chooses to disclose the difference. I believe that is the formula that most online mortgage calculators use. If the interest is compounded daily , the mortgage payment __should__ be computed as above, but r is (1 + i/365)^(365/12) - 1. In Excel: PMT((1 + i/365)^(365/12) - 1, n,, -LOAN). In Excel, r can also be computed using FV(i/365, 365/12,, -1) - 1. However, I cannot say if any lenders use the latter formulas to determine the payment when interest is compounded daily. Instead, the payment might still be determined by the compounded-monthly formula, and the daily interest rate might be as simple as i/365. Either or both can result in a larger last payment, which I believe the lender would have to disclose in the Reg Z statement . Even if the lender uses the more accurate compounded-daily formula, the last payment is likely to be slightly higher -- at least in amortization tables that I have created. This is because months contain 30, 31, 28 and 29 days, not 365/12 days. Since I do not recall seeing disclosure of a balloon payment in the conventional US mortgages that I have been involved in directly or indirectly, I wonder if the lender is prepared to simply eats the extra interest in the last period . Many mortgages are paid off before the last scheduled payment anyway. .

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