What Is an Amortization Schedule?

Amortizing loans feature level payment amounts over the life of the loan, but with varying proportions of interest and principal making up each payment. A traditional mortgage is a prime example of such a loan.

A loan amortization schedule represents the complete table of periodic loan payments, showing the amount of principal and interest that comprise each level payment until the loan is paid off at the end of its term. Early in the schedule, the majority of each payment goes toward interest; later in the schedule, the majority of each payment begins to cover the loan’s remaining principal.

Understanding an Amortization Schedule

If you are taking out a mortgage or auto loan, your lender should provide you with a copy of your loan amortization schedule so you can see at a glance what the loan will cost and how the principal and interest will be broken down over its life.

In a loan amortization schedule, the percentage of each payment that goes toward interest diminishes a bit with each payment and the percentage that goes toward principal increases. Take, for example, a loan amortization schedule for a $165,000, 30-year fixed-rate mortgage with a 4.5% interest rate:

Amortization schedules can be customized based on your loan and your personal circumstances. With more sophisticated amortization calculators, like the templates you can find in Excel you can compare how making accelerated payments can accelerate your amortization. If for example, you are expecting an inheritance, or you get a set yearly bonus, you can use these tools to compare how applying that windfall to your debt can affect your loan’s maturity date and your interest cost over the life of the loan.

In addition to mortgages, car loans and personal loans are also amortizing for a term set in advance, at a fixed interest rate with a set monthly payment. The terms vary depending on the asset. Most conventional home loans are 15- or 30-year terms. Car owners often get an auto loan that will be repaid over five years or less. For personal loans, three years is a common term.

Formulas Used in Amortization Schedules

Borrowers and lenders use amortization schedules for installment loans that have payoff dates that are known at the time the loan is taken out, such as a mortgage or a car loan. There are specific formulas that are used to develop a loan amortization schedule. These formulas may be built into the software you are using, or you may need to set up your amortization schedule from scratch.

If you know the term of a loan and the total periodic payment amount, there is an easy way to calculate a loan amortization schedule without resorting to the use of an online amortization schedule or calculator. The formula to calculate the monthly principal due on an amortized loan is as follows:

Principal Payment = Total Monthly Payment – [Outstanding Loan Balance x (Interest Rate / 12 Months)]

To illustrate, imagine a loan has a 30-year term, a 4.5% interest rate, and a monthly payment of $1,266.71. Starting in month one, multiply the loan balance ($250,000) by the periodic interest rate. The periodic interest rate is one-twelfth of 4.5% (or 0.00375), so the resulting equation is $250,000 x 0.00375 = $937.50. The result is the first month’s interest payment. Subtract that amount from the periodic payment ($1,266.71 – $937.50) to calculate the portion of the loan payment allocated to the principal of the loan’s balance ($329.21).

To calculate the next month’s interest and principal payments, subtract the principal payment made in month one ($329.21) from the loan balance ($250,000) to get the new loan balance ($249,670.79), and then repeat the steps above to calculate which portion of the second payment is allocated to interest and which is allocated to the principal. You can repeat these steps until you have created an amortization schedule for the full life of the loan.

An Easier Way to Calculate an Amortization Schedule

Calculating an amortization schedule is as simple as entering the principal, interest rate, and loan term into a loan amortization calculator. But you can also calculate it by hand if you know the rate on the loan, the principal amount borrowed, and the loan term.

How to Calculate the Total Monthly Payment

Typically, the total monthly payment is specified by your lender when you take out a loan. However, if you are attempting to estimate or compare monthly payments based on a given set of factors, such as loan amount and interest rate, you may need to calculate the monthly payment as well.

If you need to calculate the total monthly payment for any reason, the formula is as follows:

Total Monthly Payment = Loan Amount [ i (1+i) ^ n / ((1+i) ^ n) – 1) ]

where:

• i = monthly interest rate. You’ll need to divide your annual interest rate by 12. For example, if your annual interest rate is 6%, your monthly interest rate will be .005 (.06 annual interest rate / 12 months).
• n = number of payments over the loan’s lifetime. Multiply the number of years in your loan term by 12. For example, a 30-year mortgage loan would have 360 payments (30 years x 12 months).

Using the same example from above, we will calculate the monthly payment on a $250,000 loan with a 30-year term and a 4.5% interest rate. The equation gives us $250,000 [(0.00375 (1.00375) ^ 360) / ((1.00375) ^ 360) – 1) ] = $1,266.71. The result is the total monthly payment due on the loan, including both principal and interest charges.

30-Year vs. 15-Year Amortization Table

If a borrower chooses a shorter amortization period for their mortgage—for example, 15 years—they will save considerably on interest over the life of the loan, and they will own the house sooner. That’s because they’ll make fewer payments for which interest will be amortized. Additionally, interest rates on shorter-term loans are often at a discount compared to longer-term loans.

There is a tradeoff, however. A shorter amortization window increases the monthly payment due on the loan. Short amortization mortgages are good options for borrowers who can handle higher monthly payments without hardship; they still involve making 180 sequential payments (15 years x 12 months).

It’s important to consider whether or not you can maintain that level of payment based on your current income and budget.

Using an amortization calculator can help you compare loan payments against potential interest savings for a shorter amortization to decide which option suits you best. Here’s what a $500,000 loan with a 6% interest rate would look like, with a hypothetical 30-year and 15-year schedule to compare:

What is an Autonomous Expenditure?

An autonomous expenditure describes the components of an economy’s aggregate expenditure that are not impacted by that same economy’s real level of income. This type of spending is considered automatic and necessary, whether occurring at the government level or the individual level. The classical economic theory states that any rise in autonomous expenditures will create at least an equivalent rise in aggregate output, such as GDP, if not a greater increase.

Understanding Autonomous Expenditure

An autonomous expenditure obligation must be met regardless of income. It is considered independent in nature, as the need does not vary with incomes. Often, these expenses are associated with the ability to maintain a state of autonomy. Autonomy, in regard to nations, includes the ability to be self-governing. For individuals, it refers to the ability to function within a certain level of societally acceptable independence.

To be considered an autonomous expenditure, the spending must generally be deemed necessary to maintain a base level of function or, in an individual sense, survival. Often, these expenses do not vary regardless of personal disposable income or national income. Autonomous expenditure is tied to autonomous consumption, including all of the financial obligations required to maintain a basic standard of living. All expenses beyond these are considered part of induced consumption, which is affected by changes in disposable income.

In cases in which personal income is insufficient, autonomous expenses still must be paid. These needs can be met through the use of personal savings, consumer borrowing mechanisms such as loans and credit cards, or various social services.

Autonomous Expenditures and Income Levels

While the obligations that qualify as autonomous expenditures do not vary, the amount of income directed toward them can. For example, in an individual sense, the need for food qualifies as an autonomous expenditure, though the need can be fulfilled in a variety of manners, ranging from the use of food stamps to eating every meal at a five-star restaurant. Even though income level may affect how the need is met, the need itself does not change.

Governments and Autonomous Expenditures

The vast majority of government spending qualifies as autonomous expenditures. This is due to the fact that the spending often relates strongly to the efficient running of a nation, making some of the expenditures required in order to maintain minimum standards.

Factors Affecting Autonomous Expenditures

Technically, autonomous expenditures are not affected by external factors. In reality, however, several factors can affect autonomous expenditures. For example, interest rates have a significant effect on consumption in an economy. High interest rates can tamp down on consumption while low interest rates can spur it. In turn, this affects spending within an economy.

Trade policies between countries can also affect autonomous expenditures made by their citizens. If a producer of cheap goods imposes duties on exports, then it would have the effect of making finished products for outside geographies more expensive. Governments can also impose controls on an individual’s autonomous expenditures through taxes. If a basic household good is taxed and no substitutes are available, then the autonomous expenditure pertaining to it may decrease.

Examples of Autonomous Expenditure

Some of the spending classes that are considered independent of income levels, which can be counted as either individual income or taxation income, are government expenditures, investments, exports, and basic living expenses such as food and shelter.

What Is an Anomaly?

In economics and finance, an anomaly is when the actual result under a given set of assumptions is different from the expected result predicted by a model. An anomaly provides evidence that a given assumption or model does not hold up in practice. The model can either be a relatively new or older model.

Understanding Anomalies

In finance, two common types of anomalies are market anomalies and pricing anomalies. Market anomalies are distortions in returns that contradict the efficient market hypothesis (EMH). Pricing anomalies are when something—for example, a stock—is priced differently than how a model predicts it will be priced.

Common market anomalies include the small-cap effect and the January effect. The small-cap effect refers to the small company effect, where smaller companies tend to outperform larger ones over time. The January effect refers to the tendency of stocks to return much more in the month of January than in others.

Anomalies also often occur with respect to asset pricing models, in particular, the capital asset pricing model (CAPM). Although the CAPM was derived by using innovative assumptions and theories, it often does a poor job of predicting stock returns. The numerous market anomalies that were observed after the formation of the CAPM helped form the basis for those wishing to disprove the model. Although the model may not hold up in empirical and practical tests, it still does hold some utility.

Anomalies tend to be few and far between. In fact, once anomalies become publicly known, they tend to quickly disappear as arbitragers seek out and eliminate any such opportunity from occurring again.

Types of Market Anomalies

In financial markets, any opportunity to earn excess profits undermines the assumptions of market efficiency, which states that prices already reflect all relevant information and so cannot be arbitraged.

January Effect

The January effect is a rather well-known anomaly. According to the January effect, stocks that underperformed in the fourth quarter of the prior year tend to outperform the markets in January. The reason for the January effect is so logical that it is almost hard to call it an anomaly. Investors will often look to jettison underperforming stocks late in the year so that they can use their losses to offset capital gains taxes (or to take the small deduction that the IRS allows if there is a net capital loss for the year). Many people call this event tax-loss harvesting.

As selling pressure is sometimes independent of the company’s actual fundamentals or valuation, this “tax selling” can push these stocks to levels where they become attractive to buyers in January.

Likewise, investors will often avoid buying underperforming stocks in the fourth quarter and wait until January to avoid getting caught up in the tax-loss selling. As a result, there is excess selling pressure before January and excess buying pressure after Jan. 1, leading to this effect.

September Effect

The September effect refers to historically weak stock market returns for the month of September. There is a statistical case for the September effect depending on the period analyzed, but much of the theory is anecdotal. It is generally believed that investors return from summer vacation in September ready to lock in gains as well as tax losses before the end of the year.

There is also a belief that individual investors liquidate stocks going into September to offset schooling costs for children. As with many other calendar effects, the September effect is considered a historical quirk in the data rather than an effect with any causal relationship. 

Days of the Week Anomalies

Efficient market supporters hate the “Days of the Week” anomaly because it not only appears to be true, but it also makes no sense. Research has shown that stocks tend to move more on Fridays than Mondays and that there is a bias toward positive market performance on Fridays. It is not a huge discrepancy, but it is a persistent one.

The Monday effect is a theory which states that returns on the stock market on Mondays will follow the prevailing trend from the previous Friday. Therefore, if the market was up on Friday, it should continue through the weekend and, come Monday, resume its rise. The Monday effect is also known as the “weekend effect.”

On a fundamental level, there is no particular reason that this should be true. Some psychological factors could be at work. Perhaps an end-of-week optimism permeates the market as traders and investors look forward to the weekend. Alternatively, perhaps the weekend gives investors a chance to catch up on their reading, stew and fret about the market, and develop pessimism going into Monday.

Superstitious Indicators

Aside from calendar anomalies, there are some non-market signals that some people believe will accurately indicate the direction of the market. Here is a short list of superstitious market indicators:

• The Super Bowl Indicator: When a team from the old American Football League wins the game, the market will close lower for the year. When an old National Football League team wins, the market will end the year higher. Silly as it may seem, the Super Bowl indicator was correct almost three-quarters of the time over a 53-year period ending in 2021. However, the indicator has one limitation: It contains no allowance for an expansion-team victory!
• The Hemline Indicator: The market rises and falls with the length of skirts. Sometimes this indicator is referred to as the “bare knees, bull market” theory. To its merit, the hemline indicator was accurate in 1987, when designers switched from miniskirts to floor-length skirts just before the market crashed. A similar change also took place in 1929, but many argue as to which came first, the crash or the hemline shifts.
• The Aspirin Indicator: Stock prices and aspirin production are inversely related. This indicator suggests that when the market is rising, fewer people need aspirin to heal market-induced headaches. Lower aspirin sales should indicate a rising market.

What Is Add-On Interest?

Add-on interest is a method of calculating the interest to be paid on a loan by combining the total principal amount borrowed and the total interest due into a single figure, then multiplying that figure by the number of years to repayment. The total is then divided by the number of monthly payments to be made. The result is a loan that combines interest and principal into one amount due.

This method of calculating the payment on a loan is substantially more expensive for the borrower than the traditional simple interest calculation and is rarely used in consumer loans. Most loans use simple interest, where the interest charged is based on the amount of principal that is owed after each payment is made. Add-on interest loans may occasionally be used in short-term installment loans and in loans to subprime borrowers.

Understanding Add-On Interest

In simple interest loans, where the interest charged is based on the amount of principal that is owed after each payment is made, the payments may be identical in size from month to month, but that is because the principal paid increases over time while the interest paid decreases.

If the consumer pays off a simple interest loan early, the savings can be substantial. The number of interest payments that would have been attached to future monthly payments has been effectively erased.

But in an add-on interest loan, the amount owed is calculated upfront as a total of the principal borrowed plus annual interest at the stated rate, multiplied by the number of years until the loan is fully repaid. That total owed is then divided by the number of months of payments due in order to arrive at a monthly payment figure.

This means that the interest owed each month remains constant throughout the life of the loan. The interest owed is much higher, and, even if the borrower pays off the loan early, the interest charged will be the same.

Example of Add-On Interest

Say a borrower obtains a $25,000 loan at an 8% add-on interest rate that is to be repaid over four years.

• The amount of principal to be paid each month would be $520.83 ($25,000 / 48 months).
• The amount of interest owed each month would be $166.67 ($25,000 x 0.08 / 12).
• The borrower would be required to make payments of $687.50 each month ($520.83 + $166.67).
• The total interest paid would be $8,000 ($25,000 x 0.08 x 4).

Using a simple interest loan payment calculator, the same borrower with the same 8% interest rate on a $25,000 loan over four years would have required monthly payments of $610.32. The total interest due would be $3,586.62.

The borrower would pay $4,413.38 more for the add-on interest loan compared to the simple interest loan, that is, if the borrower did not pay off the loan early, reducing the total interest even more.

When researching a consumer loan, especially if you have poor credit, read the fine print carefully to determine whether the lender is charging you add-on interest. If that is the case, continue searching until you find a loan that charges simple interest.