What Is an Annualized Rate of Return?

An annualized rate of return is calculated as the equivalent annual return an investor receives over a given period. The Global Investment Performance Standards dictate that returns of portfolios or composites for periods of less than one year may not be annualized. This prevents “projected” performance in the remainder of the year from occurring.

Understanding Annualized Rate

Annualized returns are returns over a period scaled down to a 12-month period. This scaling process allows investors to objectively compare the returns of any assets over any period.

Calculation Using Annual Data

Calculating the annualized performance of an investment or index using yearly data uses the following data points:

P = principal, or initial investment

G = gains or losses

n = number of years

AP = annualized performance rate

The generalized formula, which is exponential to take into account compound interest over time, is:

AP = ((P + G) / P) ^ (1 / n) – 1

Annualized Rate of Return Examples

For example, assume an investor invested $50,000 into a mutual fund and, four years later, the investment is worth $75,000. This is a $25,000 gain in four years. Thus, the annualized performance is:

AP = (($50,000 + $25,000) / $50,000) ^ (1/4) – 1

In this example, the annualized performance is 10.67 percent.

A $25,000 gain on a $50,000 investment over four years is a 50 percent return. It is inaccurate to say the annualized return is 12.5 percent, or 50 percent divided by four because this does not take into effect compound interest. If reversing the 10.67 percent result to compound over four years, the result is exactly what is expected:

$75,000 = $50,000 x (1 + 10.67%) ^ 4

It is important not to confuse annualized performance with annual performance. The annualized performance is the rate at which an investment grows each year over the period to arrive at the final valuation. In this example, a 10.67 percent return each year for four years grows $50,000 to $75,000. But this says nothing about the actual annual returns over the four-year period. Returns of 4.5 percent, 13.1 percent, 18.95 percent and 6.7 percent grow $50,000 into approximately $75,000. Also, returns of 15 percent, -7.5 percent, 28 percent, and 10.2 percent provide the same result.

Using Days in the Calculation

Industry standards for most investments dictate the most precise form of annualized return calculation, which uses days instead of years. The formula is the same, except for the exponent:

AP = ((P + G) / P) ^ (365 / n) – 1

Assume from the previous example that the fund returned $25,000 over a 1,275-day period. The annualized return is then:

AP = (($50,000 + $25,000) / $50,000) ^ (365/1275) – 1

The annualized performance in this example is 12.31 percent.

What Is Accumulated Depreciation?

Accumulated depreciation is the cumulative depreciation of an asset up to a single point in its life. Accumulated depreciation is a contra asset account, meaning its natural balance is a credit that reduces the overall asset value.

Understanding Accumulated Depreciation

The matching principle under generally accepted accounting principles (GAAP) dictates that expenses must be matched to the same accounting period in which the related revenue is generated. Through depreciation, a business will expense a portion of a capital asset’s value over each year of its useful life. This means that each year a capitalized asset is put to use and generates revenue, the cost associated with using up the asset is recorded.

Accumulated depreciation is the total amount an asset has been depreciated up until a single point. Each period, the depreciation expense recorded in that period is added to the beginning accumulated depreciation balance. An asset’s carrying value on the balance sheet is the difference between its historical cost and accumulated depreciation. At the end of an asset’s useful life, its carrying value on the balance sheet will match its salvage value.

When recording depreciation in the general ledger, a company debits depreciation expense and credits accumulated depreciation. Depreciation expense flows through to the income statement in the period it is recorded. Accumulated depreciation is presented on the balance sheet below the line for related capitalized assets. The accumulated depreciation balance increases over time, adding the amount of depreciation expense recorded in the current period.

How to Calculate Accumulated Depreciation

There are several acceptable methods for calculating depreciation. These methods are allowable under Generally Accepted Accounting Principles (GAAP). A company may select the depreciation method they wish to use.

Straight-Line Method

Under the straight-line method of accounting, a company deducts the asset’s salvage value from the purchase price to find a depreciable base. Then, this base is accumulated evenly over the anticipated useful life of the asset. The straight-line method formula is:

Annual Accumulated Depreciation = (Asset Value – Salvage Value) / Useful Life in Years

Imagine Company ABC buys a building for $250,000. The building is expected to be useful for 20 years with a value of $10,000 at the end of the 20th year. The depreciable base for the building is $240,000 ($250,000 – $10,000). Divided over 20 years, the company would recognized $20,000 of accumulated depreciation every year. 

Declining Balance Method

Under the declining balance method, depreciation is recorded as a percentage of the asset’s current book value. Because the same percentage is used in every year while the current book value decreases, the amount of depreciation decreases each year. Even though accumulated depreciation will still increase, the amount of accumulated depreciation will decrease each year.

Annual Accumulated Depreciation = Current Book Value * Depreciation Rate

For example, imagine Company ABC buys a company vehicle for $10,000 with no salvage value at the end of its life. The company decided it would depreciate 20% of the book value each year. In Year 1, Company ABC would recognize $2,000 ($10,000 * 20%) of depreciation and accumulated depreciation. In Year 2, Company ABC would recognize $1,600 (($10,000 – $2,000) * 20%).

Double-Declining Balance Method

Under the double-declining balance (also called accelerated depreciation), a company calculates what it’s depreciation would be under the straight-line method. Then, the company doubles the depreciation rate, keeps this rate the same across all years the asset is depreciated, and continues to accumulate depreciation until the salvage value is reached. The percentage can simply be calculated as twice of 100% divided by the number of years of useful life.

Double-Declining Balance Method Rate = (100% / Useful Life In Years) * 2

Double-Declining Balance Method = Depreciable Amount * Double-Declining Balance Method Rate

Let’s imagine Company ABC’s building they purchased for $250,000 with a $10,000 salvage value. Under the straight-line method, the company recognized 5% (100% depreciation / 20 years); therefore, it would use 10% as the depreciation base for the double-declining balance method. The company would recognize $24,000 ($240,000 depreciable base * 10%) in Year 1, and would recognize $21,600 (($240,000 depreciable base – $24,000) * 10%).

Sum-of-the-Years’ Digits Method

Under the sum-of-the-years’ digits method, a company strives to record more depreciation earlier in the life of an asset and less in the later years. This is done by adding up the digits of the useful years, then depreciating based on that number of year.

Annual Accumulated Depreciation = Depreciable Base * (Inverse Year Number / Sum of Year Digits)

Company ABC purchased a piece of equipment that has a useful life of 5 years. The asset has a depreciable base of $15,000. Since the asset has a useful life of 5 years, the sum of year digits is 15 (5+4+3+2+1). The depreciation rate is then the quotient of the inverse year number (Year 1 = 5, Year 2 = 4, Year 3 = 3, etc.) divided by 15. In Year 1, the company will recognize $5,000 ($15,000 * (5/15)) of depreciation and will recognize $4,000 ($15,000 * (4/15)) in Year 2.

Units of Production Method

Under the units of production method, a company estimates the total useful output of an asset. Then, the company evaluates how many of those units were consumed each year to recognize accumulated depreciation variably based on use. The formula for the units of production method is:

Annual Accumulated Deprecation = (Number of Units Consumed / Total Units To Be Consumed) * Depreciable Base

For example, a company buys a company vehicle and plans on driving the vehicle 80,000 miles. In the first year, the company drove the vehicle 8,000 miles. Therefore, it would recognize 10% (8,000 / 80,000) of the depreciable base. In the second year, if the company drives 20,000 miles, it would recognize 25% of depreciable base as an expense in the second year, with accumulated depreciation now equal to $28,000 ($8,000 in the first year + $20,000 in the second year).

Accumulated Depreciation vs. Accelerated Depreciation

Though similar sounding in name, accumulated depreciation and accelerated depreciation refer to very different accounting concepts. Accumulated depreciation refers to the life-to-date depreciation that has been recognized that reduces the book value of an asset. On the other hand, accelerated depreciation refers to a method of depreciation where a higher amount of depreciation is recognized earlier in an asset’s life.

Since accelerated depreciation is an accounting method for recognizing depreciation, the result of accelerated depreciation is to book accumulated depreciation. Under this method, the amount of accumulated depreciation accumulates faster during the early years of an asset’s life and accumulates slower later. The philosophy behind accelerated depreciation is assets that are newer (i.e. a new company vehicle) are often used more than older assets because they are in better condition and more efficient. 

Accumulated Depreciation vs. Depreciation Expense

When an asset is depreciated, two accounts are immediately impacted: accumulated depreciation and depreciation expense. The journal entry to record depreciation results in a debit to depreciation expense and a credit to accumulated depreciation. The dollar amount for each line is equal to the other.

There are two main differences between accumulated depreciation and depreciation expense. First, depreciation expense is reported on the income statement, while accumulated depreciation is reported on the balance sheet. 

Second, on a related note, the income statement does not carry from year-to-year. Activity is swept to retained earnings, and a company “resets” its income statement every year. Meanwhile, its balance sheet is a life-to-date running total that does not clear at year-end. Therefore, depreciation expense is recalculated every year, while accumulated depreciation is always a life-to-date running total.

Special Considerations

Accounting Adjustments/Changes in Estimate

Because the depreciation process is heavily rooted with estimates, it’s common for companies to need to revise their guess on the useful life of an asset’s life or the salvage value at the end of the asset’s life. This change is reflected as a change in accounting estimate, not a change in accounting principle. For example, say a company was depreciating a $10,000 asset over its five year useful life with no salvage value. Using the straight-line method, accumulated depreciation of $2,000 is recognized.

After two years, the company realizes the remaining useful life is not three years but instead six years. Under GAAP, the company does not need to retroactively adjust financial statements for changes in estimates. Instead, the company will change the amount of accumulated depreciation recognized each year. 

In this example, since the asset now has a $6,000 net book value ($10,000 purchase price less $4,000 of accumulated depreciation booked in the first two years), the company will now recognized $1,000 of accumulated depreciation for the next six years. 

Half-Year Recognition

A commonly practiced strategy for depreciating an asset is to recognize a half year of depreciation in the year an asset is acquired and a half year of depreciation in the last year of an asset’s useful life. This strategy is employed to more fairly allocate depreciation expense and accumulated depreciation in years when an asset may only be used part of a year. 

For example, Company A buys a company vehicle in Year 1 with a five year useful life. Regardless of the month, the company will recognize six months worth of depreciation in Year 1. The company will also recognize a full year of depreciation in Year 2 – 5. Then, the company will recognize the final half year of depreciation in Year 6. Although the asset only had a useful life of five years, it is argued that the asset wasn’t used for the entirety of Year 1 nor the entirety of Year 6.

Example of Accumulated Depreciation

Company A buys a piece of equipment with a useful life of 10 years for $110,000. The equipment is estimated to have a salvage value of $10,000. The equipment is going to provide the company with value for the next 10 years, so the company expenses the cost of the equipment over the next 10 years. Straight-line depreciation is calculated as (($110,000 – $10,000) / 10), or $10,000 a year. This means the company will depreciate $10,000 for the next 10 years until the book value of the asset is $10,000.

Each year the contra asset account referred to as accumulated depreciation increases by $10,000. For example, at the end of five years, the annual depreciation expense is still $10,000, but accumulated depreciation has grown to $50,000. That is, accumulated depreciation is a cumulative account. It is credited each year as the value of the asset is written off and remains on the books, reducing the net value of the asset, until the asset is disposed of or sold. It is important to note that accumulated depreciation cannot be more than the asset’s historical cost even if the asset is still in use after its estimated useful life.

The Bottom Line

Many companies rely on capital assets such as buildings, vehicles, equipment, and machinery as part of their operations. In accordance with accounting rules, companies must depreciate these assets over their useful lives. As a result, companies must recognize accumulated depreciation, the sum of depreciation expense recognized over the life of an asset. Accumulated depreciation is reported on the balance sheet as a contra asset that reduces the net book value of the capital asset section. 

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: