What is loan amortization?
To paraphrase Wikipedia loan amortization refers to the process of systematically paying off a debt over time through regular, scheduled payments. A portion of each payment covers current interest charges while the remaining amount is applied towards the principal balance.
An amortization schedule is a report that, at minimum, shows the portion of each payment allocated to principal and interest as well as the remaining principal loan balance. The schedule may be forward looking - that is it shows a "projected" schedule of expected payments. Or it may be an actual schedule - one that shows the payment amounts and dates actually paid.
This website has calculators capable of creating either type of schedule (see the listings to the left).
This page discusses how amortization works. What you should know before taking on a loan. And the loan features that will save the debtor money. Trust me, it just not about getting the lowest possible interest rate.
We'll cover (click to scroll to):
- special cases of dates & 1st period interest
- nine loan amortization methods (calculation methods)
- points, fees and APR
- negative amortization
For accurate amortization calculations, a calculator needs to give the user the the ability to specify both the loan origination date as well as the first payment due date.
The length of time between when the money is lent and the time the first payment is due is almost never going to be equal to the stated payment frequency. That is, if the schedule payment frequency is monthly, the first period will likely be longer or shorter than one month. This difference is commonly called an odd length first period.
Supporting odd length first periods results in more accurate calculations, but you'll see interest charges that do not match other calculators.
Long first period
A long first period occurs when the period between the loan date and the first payment date is longer than the selected payment frequency. Example: Loan originates on May 16 and the first payment is due on July 1st (assuming a monthly payment frequency). The interest due for these extra or odd days can be calculated in one of four ways.
- None - free money! No interest calculated on the odd days
- With first - odd day interest paid with first payment due. Payment will be larger than the other periodic payments.
- With origination - odd day interest is due when the loan originates - commonly known as "prepaid interest"
- Amortized - a small amount of odd day interest is paid with each payment. The calculator increases all payments so they are equal.
Short first period
A short first period occurs when the period between the loan date and the first payment date is shorter than the selected payment frequency. There are three ways in which a user might want a calculator to handle a short first period scenario:
- No payment reduction - the calculator calculates what is considered to be a "normal" normal payment amount and uses it for the first payment. The last loan payment is reduced to compensate for the short period
- Reduce first - the first payment is reduced to compensate for the short period
- Reduce all - all payments are reduced to compensate for the short period.
Here's a more formal definition of odd days interest from the Financial Dictionary.
One more comment about dates.
By default, the schedule's totals are usually calculated as of December 31.
But some taxpayers pay taxes based on a different year-end. To accomodate the needs of these taxpayers, a good calculator will support annual and cumulative totals as of any month end.
Nine Loan Amortization Methods
Normal Loan Amortization
If in doubt, use this setting when amortizing a loan. In the US at least, nearly all loans use the "normal" method.
These are the characteristics of a normal loan or mortgage:
- They have "level payments" i.e., the scheduled periodic payment amount does not change. (With the possible allowance, as discussed above, for odd day interest.)
- The interest amount paid declines each period as the loan balance is being paid down.
- Thus, the principal amount paid each period increases to keep the payment amount level.
- There may be a slight adjustment ("rounding") of the final payment so that the loan is brought to a 0 balance.
The next method, consumers will want to avoid.
Rule-of-78s Payment Schedule
The Rule-of-78s method front loads the interest due. That is, the debtor pays more interest early in the payment schedule and less interest later when compared to a "normal" loan.
Both the periodic payment amount and the total loan interest due are the same for both the Rule-of-78s and the "normal" methods. The only difference is how the interest gets allocated each period.
The blog post here thoroughly explains the Rule-of-78s amortization and why, as a consumer, you may want to avoid such loans.
For the lowest periodic payment, get a loan using the next payback method. There's only one catch...
Some loans require the borrower to pay only the interest due each period. Such loans are known as "interest-only loans"
These are the characteristics of an interest-only loan or mortgage:
- The periodic payment amount generally does not change.
- The interest amount paid each period is the same because no principal is paid, the loan balance does not change.
- The entire principal balance plus the last period's interest is due with the last payment.
If you think that interest-only loans are not very common, then think again.
Many bonds sold to investors are interest-only loans. The bond's buyers are lending the issuer money. The bonds pay the buyer a periodic coupon payment which is the interest on the debt. And as reported by Zacks the size of the bond debt in the US at "the end of 2017 was more than $40.7 trillion"
That's a lot of debt financed with interest-only payments!
If you represent a bond issuer, you can prepare a bond coupon payment schedule with this site's amortization calculator. The "loan date" is the bond's issuance date and the "first payment date" is the date of the first coupon payment. Make sure to select the "Interest-Only" amortization method.
No Interest Loan Amortization
Yes, it happens! I added this amortization method to the Windows version of my calculators 20 or more years ago. Someone called me (remember phone calls?) and said he and his wife were lending money to their son and they wanted to create a payment schedule that they could agree to, the catch was, there would be no interest charged.
Many of the calculators on this site continues to support an interest-free loan.
You may ask, "Why not just enter a "0" interest rate?"
The answer is simple. If a user enters a "0" for any input, then the calculator interprets that as the unknown value. So if a user enters a "0" for the interest rate, the calculator will attempt to calculate the rate.
To get around this, select the "No Interest" option for an amortization method.
The following amortization method will save you interest charges if you can afford it.
Fixed Principal Loan Table
Before computers and calculators, that is, before it was easy to calculate a level payment amount, lenders frequently had borrowers payoff loans using the fixed principal amortization method.
Determining the payment amount requires only simple arithmetic. To calculate the payment due, first, divide the principal loan amount by the number of payments in the term and then add the periodic interest.
These are the characteristics of a fixed principal loan or mortgage:
- Payment amount start higher than a "normal" loan.
- The loans feature a declining payment amount. As the borrower pays down the principal balance, the interest due each period is reduced and therefore the payment decreases over time.
- The principal amount paid each period is fixed. The principal paid on a $1,200 loan with a term of one year will always be $100.
- The borrower pays less total interest
- There may be a slight adjustment ("rounding") of the final payment so that the loan is brought to a 0 balance.
Canadian Amortization Schedule
The Canadian amortization method is the same as the "normal amortization method" except for one detail. When the user selects the Canadian method, the calculator automatically sets the payment frequency to monthly and the compounding frequency to semiannual.
A conventional loan typically uses the same frequency for both payments and compounding.
The Canadian method, because it uses less frequent interest compounding, results in a slightly lower scheduled payment amount because the interest due is somewhat less each period when compared to the interest charges owed under monthly compounding.
For more details, here's a A Guide to Mortgage Interest Calculations in Canada.
Amortization with a Balloon Payment
Occasionally, there are times when the terms of a loan call for a payment to be calculated on a 30-year payback but the loan will come due after five years of payments (for example).
Because the payment calculation uses a 30-year term, the balance of the loan will still be substantial relative to the starting balance when the term is up in five years, and the balance is due.
Creating an amortization schedule showing the balloon payment amount is simple.
- Enter the loan amount
- Enter the interest rate
- Enter the number of payments which will be used to calculate the periodic payment due - in this case 30-years or 360 monthly payments.
- Enter "0" for the payment amount and click on "Calc." Result is the payment for a 30-year loan.
- Change the number of payments to the actual term of the loan - per this example that's 5 years or 60 payments
- Click on "Print Preview" to see your amortization schedule with a balloon payment.
Loan Schedule with Points, Fees and APR Support
Some loans require the borrower to pay an upfront charge called "points."
Why would a borrower be willing to pay an extra charge?
When the borrower pays points, the lender reduces the interest rate. Points are in essence prepaid interest (and the IRS treats them that way). One point is one percent of the loan amount. Thus, one point on a $300,000 is equal to $3,000.
The user has two choices for how to create an amortization schedule with points. Click on "Settings" and select "Points, Charges & APR Options."
If "Include dollar value of points in interest charges" is checked then the calculator calculates the dollar cost of the points, and the payment schedule shows them paid at the loan origination. The calculator also adds the cost of points to the total interest charges.
If the user didn't check this option, then the dollar value gets reported in the header only, and the amount does not get added to the total interest.
See Moving.com "What Are Mortgage Loan Points?" for more details.
Points impact the loan's annual percentage rate. If you want to check the APR (and if you are the borrower, you should), you can include a Truth-in-Lending Act compliant calculation in the schedule's footer. Just check the option "Include Regulation "Z" APR Disclosure calculation at the end of the schedule?". For an accurate APR, don't forget to include any fees in "Other charges & fees (for APR calculation)?" input.
Negative Amortization Calculation
Users frequently tell me they use this site's calculator to "check their lender's payment amount."
That's fine, of course. But all borrowers should also understand, there is no such thing as a "correct payment amount." The only payment amount of concern is the amount agreed to between the lender and borrower. All things being equal if the lender says the payment is $315 a month and the borrower expects it to be $311 a month, it doesn't matter - as long as they both agree on the initial period's calculated interest amount. If the parties agree on the interest calculation, then paying a slightly higher amount will pay the loan off marginally faster or result in a smaller final payment, and the total collected as interest will be slightly less.
So what does this have to do with negative amortization?
Simple, if the lender and borrower agree on an amount that is not large enough to pay the interest due it results in negative amortization.
This amortization calculator gives the user the ability to set any payment amount. Enter the agreed upon payment, and if it is less than the interest due, the calculator will create a negative amortizating loan schedule.
When the payment amount is less than the periodic interest due, the loan balance will increase each period because the interest not covered by the payment must get added to the balance.
There is nothing wrong with a negatively amortizing loan per se. However, the borrower will have to be prepared to pay a single, large payment at the end of the term.
If you are the borrower, be sure to check the last payment row of the schedule for the final payment amount, which includes the accrued interest, to see if you can handle it.
Note the negative principal amounts in the below figure.
What Do You Think?
Or what would you like to know?
While this page covers a lot of material on amortization schedules, it can't cover everything.
Let me know in the comments below what I missed. Or feel free to ask your questions and I'll answer them (to the best of my ability).