What Is Annualized Total Return?

An annualized total return is the geometric average amount of money earned by an investment each year over a given time period. The annualized return formula is calculated as a geometric average to show what an investor would earn over a period of time if the annual return was compounded.

An annualized total return provides only a snapshot of an investment’s performance and does not give investors any indication of its volatility or price fluctuations.

Understanding Annualized Total Return

To understand annualized total return, we’ll compare the hypothetical performances of two mutual funds. Below is the annualized rate of return over a five-year period for the two funds:

• Mutual Fund A Returns: 3%, 7%, 5%, 12%, and 1%
• Mutual Fund B Returns: 4%, 6%, 5%, 6%, and 6.7%

Both mutual funds have an annualized rate of return of 5.5%, but Mutual Fund A is much more volatile. Its standard deviation is 4.2%, while Mutual Fund B’s standard deviation is only 1%. Even when analyzing an investment’s annualized return, it is important to review risk statistics.

Annualized Return Formula and Calculation

The formula to calculate annualized rate of return needs only two variables: the returns for a given period of time and the time the investment was held. The formula is:


$\begin{aligned} \text{Annualized Return} = &\big ( (1 + r_1 ) \times (1 + r_2) \times (1 + r_3) \times \\ &\dots \times (1 + r_n) \big ) ^ \frac{1}{n} – 1 \\ \end{aligned}$Annualized Return=​((1+r1​)×(1+r2​)×(1+r3​)×⋯×(1+rn​))n1​−1​

For example, take the annual rates of returns of Mutual Fund A above. An analyst substitutes each of the “r” variables with the appropriate return, and “n” with the number of years the investment was held. In this case, five years. The annualized return of Mutual Fund A is calculated as:


$\begin{aligned} \text{Annualized Return} &= \big ( (1 + .03) \times (1 + .07) \times (1 + .05) \times \\ &\quad \quad (1 + .12) \times (1 + .01) \big ) ^ \frac{1}{5} -1 \\ &= 1.309 ^ {0.20} – 1 \\ &= 1.0553 – 1 \\ &= .0553, \text{or } 5.53\% \\ \end{aligned}$Annualized Return​=((1+.03)×(1+.07)×(1+.05)×(1+.12)×(1+.01))51​−1=1.3090.20−1=1.0553−1=.0553,or 5.53%​

An annualized return does not have to be limited to yearly returns. If an investor has a cumulative return for a given period, even if it is a specific number of days, an annualized performance figure can be calculated; however, the annual return formula must be slightly adjusted to:


$\begin{aligned} &\text{Annualized Return} = ( 1 + \text{Cumulative Return} ) ^ \frac {365}{ \text{Days Held} } – 1 \\ \end{aligned}$​Annualized Return=(1+Cumulative Return)Days Held365​−1​

For example, assume a mutual fund was held by an investor for 575 days and earned a cumulative return of 23.74%. The annualized rate of return would be:


$\begin{aligned} \text{Annualized Return} &= ( 1 + .2374) ^ \frac{365}{575} – 1 \\ &= 1.145 – 1 \\ &= .145, \text{or } 14.5\% \\ \end{aligned}$Annualized Return​=(1+.2374)575365​−1=1.145−1=.145,or 14.5%​

Difference Between Annualized Return and Average Return

Calculations of simple averages only work when numbers are independent of each other. The annualized return is used because the amount of investment lost or gained in a given year is interdependent with the amount from the other years under consideration because of compounding.

For example, if a mutual fund manager loses half of her client’s money, she has to make a 100% return to break even. Using the more accurate annualized return also gives a clearer picture when comparing various mutual funds or the return of stocks that have traded over different time periods. 

Reporting Annualized Return

According to the Global Investment Performance Standards (GIPS)—a set of standardized, industry-wide principles that guide the ethics of performance reporting—any investment that does not have a track record of at least 365 days cannot “ratchet up” its performance to be annualized.

Thus, if a fund has been operating for only six months and earned 5%, it is not allowed to say its annualized performance is approximately 10% since that is predicting future performance instead of stating facts from the past. In other words, calculating an annualized rate of return must be based on historical numbers.

The Bottom Line

Annualized total return represents the geometric average amount that an investment has earned each year over a specific period. By calculating a geometric average, the annualized total return formula accounts for compounding when depicting the yearly earnings that the investment would generate over the holding period. While the metric provides a useful snapshot of an investment’s performance, it does not reveal volatility and price fluctuations.

What Is an Adjusting Journal Entry?

An adjusting journal entry is an entry in a company’s general ledger that occurs at the end of an accounting period to record any unrecognized income or expenses for the period. When a transaction is started in one accounting period and ended in a later period, an adjusting journal entry is required to properly account for the transaction.

Adjusting journal entries can also refer to financial reporting that corrects a mistake made previously in the accounting period.

Understanding Adjusting Journal Entries

The purpose of adjusting entries is to convert cash transactions into the accrual accounting method. Accrual accounting is based on the revenue recognition principle that seeks to recognize revenue in the period in which it was earned, rather than the period in which cash is received.

As an example, assume a construction company begins construction in one period but does not invoice the customer until the work is complete in six months. The construction company will need to do an adjusting journal entry at the end of each of the months to recognize revenue for 1/6 of the amount that will be invoiced at the six-month point.

An adjusting journal entry involves an income statement account (revenue or expense) along with a balance sheet account (asset or liability). It typically relates to the balance sheet accounts for accumulated depreciation, allowance for doubtful accounts, accrued expenses, accrued income, prepaid expenses, deferred revenue, and unearned revenue.

Income statement accounts that may need to be adjusted include interest expense, insurance expense, depreciation expense, and revenue. The entries are made in accordance with the matching principle to match expenses to the related revenue in the same accounting period. The adjustments made in journal entries are carried over to the general ledger that flows through to the financial statements.

Types of Adjusting Journal Entries

In summary, adjusting journal entries are most commonly accruals, deferrals, and estimates.

Accruals

Accruals are revenues and expenses that have not been received or paid, respectively, and have not yet been recorded through a standard accounting transaction. For instance, an accrued expense may be rent that is paid at the end of the month, even though a firm is able to occupy the space at the beginning of the month that has not yet been paid.

Deferrals

Deferrals refer to revenues and expenses that have been received or paid in advance, respectively, and have been recorded, but have not yet been earned or used. Unearned revenue, for instance, accounts for money received for goods not yet delivered.

Estimates

Estimates are adjusting entries that record non-cash items, such as depreciation expense, allowance for doubtful accounts, or the inventory obsolescence reserve.

Why Are Adjusting Journal Entries Important?

Because many companies operate where actual delivery of goods may be made at a different time than payment (either beforehand in the case of credit or afterward in the case of pre-payment), there are times when one accounting period will end with such a situation still pending. In such a case, the adjusting journal entries are used to reconcile these differences in the timing of payments as well as expenses. Without adjusting entries to the journal, there would remain unresolved transactions that are yet to close.

Example of an Adjusting Journal Entry

For example, a company that has a fiscal year ending December 31 takes out a loan from the bank on December 1. The terms of the loan indicate that interest payments are to be made every three months. In this case, the company’s first interest payment is to be made March 1. However, the company still needs to accrue interest expenses for the months of December, January, and February.

Since the firm is set to release its year-end financial statements in January, an adjusting entry is needed to reflect the accrued interest expense for December. To accurately report the company’s operations and profitability, the accrued interest expense must be recorded on the December income statement, and the liability for the interest payable must be reported on the December balance sheet. The adjusting entry will debit interest expense and credit interest payable for the amount of interest from December 1 to December 31.

What Is an Annuity Table?

An annuity table is a tool for determining the present value of an annuity or other structured series of payments. Such a tool, used by accountants, actuaries, and other insurance personnel, takes into account how much money has been placed into an annuity and how long it has been there to determine how much money would be due to an annuity buyer or annuitant.

Figuring the present value of any future amount of an annuity may also be performed using a financial calculator or software built for such a purpose.

How an Annuity Table Works

An annuity table provides a factor, based on time, and a discount rate (interest rate) by which an annuity payment can be multiplied to determine its present value. For example, an annuity table could be used to calculate the present value of an annuity that paid $10,000 a year for 15 years if the interest rate is expected to be 3%.

According to the concept of the time value of money, receiving a lump sum payment in the present is worth more than receiving the same sum in the future. As such, having $10,000 today is better than being given $1,000 per year for the next 10 years because the sum could be invested and earn interest over that decade. At the end of the 10-year period, the $10,000 lump sum would be worth more than the sum of the annual payments, even if invested at the same interest rate.

Annuity Table and the Present Value of an Annuity

Present Value of an Annuity Formulas

The formula for the present value of an ordinary annuity, as opposed to an annuity due, is as follows:


$\begin{aligned}&\text{P} =\text{PMT}\times\frac{ 1 – (1 + r) ^ -n}{r}\\&\textbf{where:}\\&\text{P} = \text{Present value of an annuity stream}\\&\text{PMT} =\text{Dollar amount of each annuity payment}\\&r = \text{Interest rate (also known as the discount rate)}\\&n = \text{Number of periods in which payments will be made}\end{aligned}$​P=PMT×r1−(1+r)−n​where:P=Present value of an annuity streamPMT=Dollar amount of each annuity paymentr=Interest rate (also known as the discount rate)​

Assume an individual has an opportunity to receive an annuity that pays $50,000 per year for the next 25 years, with a discount rate of 6%, or a lump sum payment of $650,000. He needs to determine the more rational option. Using the above formula, the present value of this annuity is:


$\begin{aligned}&\text{PVA} = \$50,000 \times \frac{1 – (1 + 0.06) ^ -25}{0.06} = \$639,168\\&\textbf{where:}\\&\text{PVA}=\text{Present value of annuity}\end{aligned}$​PVA=$50,000×0.061−(1+0.06)−25​=$639,168where:​

Given this information, the annuity is worth $10,832 less on a time-adjusted basis, and the individual should choose the lump sum payment over the annuity.

Note, this formula is for an ordinary annuity where payments are made at the end of the period in question. In the above example, each $50,000 payment would occur at the end of the year, each year, for 25 years. With an annuity due, the payments are made at the beginning of the period in question. To find the value of an annuity due, simply multiply the above formula by a factor of (1 + r):


$\begin{aligned}&\text{P} = \text{PMT} \times\left(\frac{1 – (1 + r) ^ -n}{r}\right) \times (1 + r)\end{aligned}$​P=PMT×(r1−(1+r)−n​)×(1+r)​

If the above example of an annuity due, its value would be:


$\begin{aligned}&\text{P}= \$50,000\\&\quad \times\left( \frac{1 – (1 + 0.06) ^ -25}{0.06}\right)\times (1 + 0.06) = \$677,518\end{aligned}$​P=$50,000​

In this case, the individual should choose the annuity due, because it is worth $27,518 more than the lump sum payment.

Present Value of an Annuity Table

Rather than working through the formulas above, you could alternatively use an annuity table. An annuity table simplifies the math by automatically giving you a factor for the second half of the formula above. For example, the present value of an ordinary annuity table would give you one number (referred to as a factor) that is pre-calculated for the (1 – (1 + r) ^ – n) / r) portion of the formula.

The factor is determined by the interest rate (r in the formula) and the number of periods in which payments will be made (n in the formula). In an annuity table, the number of periods is commonly depicted down the left column. The interest rate is commonly depicted across the top row. Simply select the correct interest rate and number of periods to find your factor in the intersecting cell. That factor is then multiplied by the dollar amount of the annuity payment to arrive at the present value of the ordinary annuity.

Below is an example of a present value of an ordinary annuity table:

What Is Adjustable Life Insurance?

Adjustable life insurance is a hybrid of term life and whole life insurance that allows policyholders the option to adjust policy features, including the period of protection, face amount, premiums, and length of the premium payment period.

Adjustable life policies also incorporate an interest-bearing savings component, known as a “cash value” account.

Understanding Adjustable Life Insurance

Adjustable life insurance differs from other life insurance products in that there is no requirement to cancel or purchase additional policies as the insured’s circumstances change. It is attractive to those who want the protection and cash value benefits of permanent life insurance yet need or want some flexibility with policy features.

Using the ability to modify premium payments and face amounts, policyholders may customize their coverage as their lives change. For example, a policyholder may want to increase the face amount upon getting married and having children. An unemployed person may want to reduce premiums to accommodate a restricted budget.

As with other permanent life insurance, adjustable life insurance has a savings component that earns cash value interest, usually at a guaranteed rate. Policyholders are permitted to make changes to critical features of their policy within limits. They may increase or decrease the premium, increase or decrease the face amount, extend or shorten the guaranteed protection period, and extend or shorten the premium payment period.

Adjustments to the policy will alter the guaranteed period of the interest rate, and changes in the length of the guarantee will change the cash value schedule. Decreasing the face amount is done upon request or in writing. However, increasing the face amount may require additional underwriting, with substantial increases requiring full medical underwriting.

Factors That Can Be Adjusted

Three factors can be changed in an adjustable life insurance policy. These are the premium, cash value, and death benefit. All three elements can be adjusted because this policy is a permanent life insurance policy and does not expire, like a term life policy.

Premiums can be changed by frequency or amount of payments, as long as you pay above the minimum cost. The policy’s cash value can be increased by upping your premium payments. You can decrease your cash amount if you withdraw funds or use the cash in the policy to pay the premiums.

Finally, you can adjust your death benefit by decreasing or adding to the amount. If you decide to add a significant amount to the death benefit due to a life event like the birth of a child, your premiums may go up based on the new benefit amount. In some cases, your policy will have to undergo additional underwriting.

Advantages and Disadvantages of Adjustable Life Insurance

Adjustable life insurance gives policyholders more flexibility than term life insurance, but it is more expensive than a simple 20- or 30-year term policy. If you plan on using adjustable life insurance as an investment vehicle, you may be better off with a tool that earns more interest. Adjustable life insurance only provides modest amounts of interest growth.

Guidelines for Life Insurance Policies and Riders

Internal Revenue Code (IRC) Section 7702 defines the characteristics of and guidelines for life insurance policies. Subsection C of this section provides guidelines for premium payments. The policyholder may not adjust the premiums in a manner that violates these guidelines. Increasing premiums may also increase the face amount to the point that it requires evidence of insurability.

However, many life insurers set parameters to prevent violations. Adjustable life insurance policies typically have optional riders. Familiar ones include the waiver of premium and accidental death and dismemberment riders.

The Bottom Line

Adjustable life policies provide the flexibility that most traditional policies do not. However, the frequency of allowable adjustments is restricted within set time frames. Requests must be made within an allotted period and meet the guidelines set by the insurer.

The variability in adjustments can create a policy that mirrors either term life insurance or whole life insurance. Effectively, adjustable life insurance policies allow policyholders to customize their life insurance to meet current or anticipated needs.

As with any kind of permanent policy, it’s critical to research every firm that’s being considered to ensure that they’re among the best life insurance companies currently operating.