How FixedRate Loan Amortization Works
or
Amortization Math: How
to construct a mortgage amortization table using formulas rather than mortgage calculators.
Mortgage Library: Ask a Mortgage Related Question: Answers: Amortization
Question:
Hello, I used your mortgage calculator and entered in a loan of $100,000 at a 7% fixed interest for 30 years. It gave me a number of $139,508.90 after 30 years, that is the total interest paid over the life of the loan. This number does not make sense because 7% of $100,000 is only $7,000 and not $139,508.90. $139,508.90 is almost 140% of the original $100,000. Please explain your reasoning for this. I look forward in hearing from you. F. Answer: Dear F., If you borrowed $100,000 from a lender with an agreement that at the end of 30 years you would repay the original loan amount plus 7%, then your total repayment would be $107,000. This is not how mortgage loans work, as mortgages utilize a nominal interest rate: the interest rate per year. The repayment process is far more complicated, and involves the concept of amortization. When money is loaned for 30 years, the mortgage agreement requires the borrower to make 360 periodic (monthly) payments to the lender. The payments must remain the same each month and fully repay both the interest and principal during the life of the loan. The quoted interest rate of 7.00% per year is compounded 12 times a year, resulting in a monthly rate of 0.58% (which is computed by dividing the note rate by 12). To calculate the interest due for a given month, the monthly rate is multiplied by the current loan balance. If you borrowed $100,000 at 7%, at the end of the first month your interest due would be $100,000 x (0.07 / 12). The process of recalculating the interest and principal every month is called amortization. To illustrate how each monthly payment is applied to your loan we need to construct an amortization table, reflecting each payment on it's own line. To build an actual amortization table on a 30year fixed $100,000.00 loan at 7.00% we need to answer the following two questions:
As soon as these questions are answered, the remaining part of each payment that goes monthly toward your loan balance is easily calculated by subtracting the interest part from the monthly payment. We will derive the equation for the monthly payment PMT in the following manner:
Now, determining the interest part of each monthly payment is simple. It is computed by multiplying the current loan balance by the effective interest rate per payment period.
Let's calculate the remaining part of the payment (the principal part), that goes toward the amount borrowed:
When your second monthly payment is due, your loan balance is: $100,000.00  $81.97 = $99,918.03. The interest part is: $99,918.03 * 0.07/12 = $582.86. The remaining part of the payment (the principal part) is: $665.30  $582.86 = $82.45. The total interest paid is: $583.33 + $582.86 = $1,166.19. Now we have the first two rows of the loan amortization table: Amortization Table
How to compute the total interest paid over the life of the loan:
We hope this is of assistance to you. Best regards, The MortgageX Team 
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