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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.
The formula for the periodic payment amount is derived as follows. For an amortization schedule, we can define a function that represents the principal amount remaining immediately after the -th payment is made. The total number of payments of the entire amortized loan is .
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 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 ...
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:
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):
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Treating a month as 30 days and a year as 360 days was devised for its ease of calculation by hand compared with manually calculating the actual days between two dates. Also, because 360 is highly factorable, payment frequencies of semi-annual and quarterly and monthly will be 180, 90, and 30 days of a 360-day year, meaning the payment amount ...