Amortization Clarified with Examples and Calculations

Amortization makes settling loans less stressful by spreading the principal across a series of fixed monthly payments so that the loan will be settled by the time you make the last monthly payment within the repayment period.

In an amortized loan, monthly payments are made up of two parts; interest and principal. Interest refers to the fee charged by the lender in exchange for the loan amount given and the principal refers to the small portion of the payable principal you are paying each month.

How amortization works

Now you know what amortization is so lets move on to how they work.

Even though monthly payments are the same for each month, the costs allocated for the interest and principal will vary.

Amortized loans have high interest costs during the early stage of their repayment period, especially in long-term loans such as 15-year or 30-year mortgage loans.

This means a considerable portion of the monthly payments you make early on will go towards the interest and not the principal. Therefore, there won’t be much progress on the repayment of the loan’s principal during the first several years.

Nevertheless, as time goes on you will see more and more of the amounts you pay going towards the principal and not the interest. And when you make the final monthly payment, your payable principal will be zero and the debt would have been completely settled.

For example, in a $100,000 15-year residential mortgage loan, a portion of the payable principal will be written off with each monthly payment you make. That’s 180 monthly payments.

By the time you make the final payment, your debt will be fully settled. That’s how amortization works.

What’s an amortization schedule?

It’s a detailed table, chart or spreadsheet that breaks down the monthly payments you have to make during the repayment period of the loan. Each row represents a single monthly payment and shows how much of it goes towards the interest and principal separately.

In addition to that, you may also see the due date of each payment, the monthly payment, the amount of interest paid so far and the principal amount to be paid in the future after each payment.

Creating such a schedule wouldn’t have been possible if the loan didn’t have a finite repayment deadline. That’s why not every loan is amortized.

The most common types of amortized loans are personal loans (as in bank loans and home mortgage loans) and auto loans (as in loans you take for the purpose of purchasing a vehicle).

Going back to the previous example, you would have to create a amortization schedule with details of all 180 monthly payments that you are legally obligated to make within the repayment period. In the case of a 30-year mortgage loan, it would be 360 payments.

Creating an amortization schedule for a loan with a fixed interest rate will be fairly straightforward but for a loan with adjustable rates, the process may be a little complicated since you can only guess or estimate the payment.

You can build an amortization schedule using one of three ways; by hand, using an online calculator or a spreadsheet software. If you are too lazy to create the entire model of the schedule from scratch in a spreadsheet, you can just copy-paste the output from online calculators.

How to calculate the monthly payment

The monthly payment of an amortized loan is determined by the three factors; loan amount, interest rate and repayment period (in years). It can be calculated using the formula given below.

Monthly payment = Loan amount / Discount factor

To calculate the discount factor you would need to know the following pieces of information.

• Number of monthly payments (n)

• Periodic interest rate (i)

To calculate n, simply multiply the number of years of the loan repayment period by 12. To calculate i, take the annual interest rate and express it as a monthly rate.

For example, if the annual rate is 6 percent, it must be expressed as .06. Then divide that number by 12, the number of payments per year.

Now that you have both n and i figured out, it’s time to calculate the discount factor or d. The formula for that is given below.

d = {[(1 + i) ^n] - 1} / [i(1 + i)^n]

Just replace i and n with the values you got in the previous step.

Now that you know the discount factor, it’s time to find the monthly payment by utilizing the previous formula.

The calculation may seem a little complicated, however, since all amortized loans are calculated with the same formula you will get used to it as you take on more and more loans in the future.

If you have a good credit score, you’ll most likely be granted lower rates and will end up saving you a lot of money.

One other solution would be to extend the loan’s repayment period, so that the monthly payable amount is diluted across the additional number of months. Just keep in mind, the more you stretch a loan, the more interest you will have to pay.

How to calculate the interest payment

Now that you know how to calculate the monthly payment, it’s time to calculate the interest only payment. For this calculation, you would need the following pieces of information.

• The interest rate

• The number of years of the repayment period

• The loan balance

• The monthly payment

There are two types of interests; simple interest and compound interest. Simple interest can be calculated using the following formula.

Interest = principal X rate X time

Here, principal refers to the loan amount, rate refers to the monthly interest rate, and time refers to the number of years of the loan repayment period.

For example, let’s say you took a $1,000 loan at 5% interest for one year. Your monthly interest would be as follows.

Interest = $1,000 X .05 X 1 = $50

This formula works great for simple loans like the one above. The problem with long-term amortized loans is that the interest amount changes each month. So how do we calculate the monthly interest of such loans?

Follow the steps below:

1. Convert the annual interest rate to a monthly rate by giving it by 12. For example, if the annual rate if 5 percent, the monthly rate would be .05 percent.

2. Multiply the monthly rate by the current loan balance to get the monthly interest amount.

3. Subtract the interest amount from the monthly payment to get the principal amount.

4. Calculate the remaining loan balance.

5. Repeat these exact steps until the loan is fully paid off.

Don’t be surprised to see a major potion of your monthly payments being allocated for interest, especially in the first several months.

As you go through the repayment period you will start to notice that the principal is being paid off more than the interest.

Types of amortized loans

Any loan with monthly installments that allows you to pay off a portion of the principal each month can be referred to as an amortized loan. The main types of amortized loans are;

• Personal loans

These are the loans offered to individuals by banks, credit unions and online lenders. Personal loans are unsecured in nature, meaning, you won’t need to place collateral. They often come with a 3-year or 5-year repayment period.

Unlike most other loans, they don’t put any restrictions on how you are allowed to use the loan funds. The only drawback is, since they are meant for individuals and not businesses, the loan amount doesn’t exceed $100,000.

• Residential mortgage loans

Residential mortgage loans are long-term loans that last either 15 or 30 years. These loans help you cover the cost of purchasing, developing and renovating residential property such as a house, apartment and etc.

After purchasing or renovating the property you may consider renting the entire or a part of the house to create an additional stream of monthly income. Most people either sell or refinance their property long before the loan is naturally settled.

• Auto loans

An auto loan is typically a 5-year loan that helps you to purchase your dream vehicle. Most people avoid extending the repayment period of such loans since the value of the loan would then exceed the vehicle’s resale value.

Non-amortizing loans

• Credit cards

Credit cards are not amortizable since they don’t require a fixed monthly payment. You are able to pay any amount as long as you are covering the minimum payment required.

• Interest-only loans

Interest-only loans are semi-amortizing loans. During the first 5-10 years of the loan, you will only be allowed to pay the interest of the loan and not the principal. Therefore, monthly payments will be much lower as well.

Once the interest-only period ends, the loan will act like any other amortizing loan out there, lowering the interest paid and putting the major portion of your monthly payments towards paying off the principal.

• Balloon loans

In balloon loans, monthly payments don’t settle the principal amount. Instead, you would have to make a large one-time principal payment at the end of the repayment period that may cause a huge gap in your cash flow.

Yes, you do make some small payments in the early years of balloon loans but they won’t be enough to settle the loan. In most cases you may have to refinance the principal payment.

Negative amortization

If you are struggling financially, lenders may allow you to make small monthly payments instead of the regular ones.

But if those payments aren’t enough to at least cover the interest portion of your regular monthly payments, you would eventually have to deal with negative amortization.

Negative amortization takes place when a borrower’s loan balance goes up over time due to unpaid interests instead of decreasing.

All unpaid interest gets added to the principal amount so when paying back the loan, you would have to pay interest for both the original principal amount and the unpaid interest.

For example, if you take on a $100,000 loan, you would see the balance increase bit by bit each month instead of decreasing. So in a year, your principal may be $125,000 or something and you would have to pay interest for the entire thing.

Depreciation vs. Amortization

While depreciation allows you to recover costs of tangible assets over their useful lifespan, amortization does the same for intangible assets. These are the assets are don’t have a physical form and yet holds value.

Examples of amortized assets are patents, trademarks, licenses, permits and etc. The only intangible asset that’s not eligible to be amortized is goodwill, since you can’t really measure it until you sell the business.

Accelerated amortization?

Straight-line depreciation is where the same amount is depreciated from an asset each year, whereas accelerated depreciation allows certain assets such as cars to be depreciated more quickly at the beginning of their lifetime than at the end.

Since depreciation expenses are tax-deductible, accelerated depreciation allows businesses to reduce their taxable income in the early years of an asset. Therefore, it’s actually a tax benefit.

But unfortunately, due to the nature of intangible assets, amortization is always calculated on a straight-line basis, meaning, the same amount will be charged every year.

Recording amortization expenses

Businesses must record their amortization expenses in accounting books, and to do that you would need the following pieces of information.

• The initial value of the asset.

• The usable lifespan of the of the asset.

• The residual value of the asset at the end of its lifespan.

Since we are working with intangible assets, calculating the initial value may be confusing and you may need the help of a small business accountant.

The usable lifespan is the number of years you can use the asset. For example, if a license is valid for X years, then it can me amortized over X years.

Any asset, whether tangible or intangible, will lose its value over time. The residual value is the worth of the asset at the end of its usable lifespan. Sometimes this may even be zero.

To calculate the amortization expense of an asset, use the following formula.

(Initial value – residual value) / lifespan = amortization expense

It works by subtracting the residual value from the asset’s initial value and then dividing the result by the lifespan or the number of usable years.

If the asset has no residual value, just divide the initial value by the lifespan and you will get the amount you can amortize each year for that asset.

You must record all amortization expenses under a line called “Depreciation and amortization” in the income statement. Be sure to debit the expense to the assets account and credit the asset.

Conclusion

The term amortization can be used in two ways; to pay off loans in equal monthly payments and a cost recovery method for intangible assets such as patents, trademarks and etc.

A loan is deemed as an amortized loan if it has a finite repayment period and a fixed interest rate. The most common types of amortized loans are home loans, auto loans and residential mortgage loans.

Interest costs will be high in the early years of long-term loans. Having a good credit score will surely aid in securing lower interest rates but if that’s not an option you could try extending the repayment period.

If you can’t make the monthly payments in full, at least pay off the interest since unpaid interest will bundle together with the principal and you would have to pay interest for the unpaid interest as well.

Amortization can also be used as a cost recovery method that allows you spread the cost of your intangible assets across the years of their usable lifespan to reduce your taxable income.

Do you have any other questions? Let me know in the comments section below.