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This amortization schedule is based on the following assumptions: First, it should be known that rounding errors occur and, depending on how the lender accumulates these errors, the blended payment (principal plus interest) may vary slightly some months to keep these errors from accumulating; or, the accumulated errors are adjusted for at the end of each year or at the final loan payment.
The formula for EMI (in arrears) is: [2] = (+) or, equivalently, = (+) (+) Where: P is the principal amount borrowed, A is the periodic amortization payment, r is the annual interest rate divided by 100 (annual interest rate also divided by 12 in case of monthly installments), and n is the total number of payments (for a 30-year loan with monthly payments n = 30 × 12 = 360).
For a 30-year loan with monthly payments, = = Note that the interest rate is commonly referred to as an annual percentage rate (e.g. 8% APR), but in the above formula, since the payments are monthly, the rate i {\displaystyle i} must be in terms of a monthly percent.
The fixed monthly payment for a fixed rate mortgage is the amount paid by the borrower every month that ensures that the loan is paid off in full with interest at the end of its term. The monthly payment formula is based on the annuity formula. The monthly payment c depends upon: r - the monthly interest rate. Since the quoted yearly percentage ...
The formula contained in this law, which determined the amount due to lenders, was called the "rule of 78" method. The reasoning behind this rule was as follows: A loan of $3000 can be broken into three $1000 payments, and a total interest of $60 into six. During the first month of the loan, the borrower has use of all three $1000 (3/3) amounts.
This monthly payment formula is easy to derive, and the derivation illustrates how fixed-rate mortgage loans work. The amount owed on the loan at the end of every month equals the amount owed from the previous month, plus the interest on this amount, minus the fixed amount paid every month. Amount owed at month 0:
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On a 30-year amortizing loan, paying equal amounts monthly, one has the following WALs, for the given annual interest rates (and corresponding monthly payments per $100,000 principal balance, calculated via an amortization calculator and the formulas below relating amortized payments, total interest, and WAL):