Accrual rate

Accrual rate describes how often interest is accrued. Accrual rates refers to a many of financial instruments including bonds, mortgages, credit cards, other types of loans and pensions. This rate is very fluctuated because of those instruments.

Meaning of accrual rate

For example, in case of credit cards it is accrued daily, while loans are usually accrued monthly. Every financial instrument that returns interest has accrual rate defined. Accrual rate is important for calculations of interest and proper understanding of the price. The price of financial instruments like bonds on the market usually includes the interest (A.W. Stark, 1989).

It is also important whether the interest increases the principal or not. In case of daily accrual rate when interest increases principal the overall cost of the e.g. loan will be much higher than in case of monthly accrual rate (P. W. Thompson, 1994).

Breaking down accrual rate

It is nesesery to know at which a financial obligation accumulates interest, because this allow to understand the price and its value. Without including the accrual rate our information about the instrument are incomplete. Taking as an example the bonds - bond's price is the sum of all its future cash flows including principal and interest. In that case, the price will include any interest accrued, but not yet paid. In like manner, calculating the payoff amount for a mortgage or other debt, accrued interest amounts must be added to the principal balance outstanding (J. R. Francis, E. L. Maydew, H. C. Sparks, 1999).

Accrual rate calculation

To calculate daily accrual rate:

$AR=IR/365$

where:

• AR - accrual rate
• IR - annual interest rate
• 365 - days in year (warning: some lenders use 30-days months and then year is 360 days)

To calculate monthly accrual rate:

$AR=IR/12$

Accrual rate in final salary scheme

A typical final salary scheme will pay a pension that depends on:

• how long you have worked for the company
• your salary when you leave the company
• scheme's accrual rate

If you are a member of the scheme, you will get for each year a proportion of final salary, which is calculated with accrual rate. Predominatingly accrual rates are expressed as fractions (1/60th or 1/80th is common) or sometimes as a percentage (e.g. 1/60th equals 1.67%).

For example, Susan retires with a salary of £30,000 after being a scheme member for 20 years. Her scheme has a 1/60th accrual rate. For every year she worked she will get 1/60th of £30,000. This is £500 for each year. So for 20 years' service, her first year's pension will be £10,000. The accrual rate is an important factor in how good a salary-related scheme actually is (M. Hanlon, 2005).

Nowadays the most common rate is probably about 1/80th, although many schemes have cut accrual rates in recent years. Very good schemes will do better with 1/60th or even 1/50th. Poorer schemes may go as low as 1/100th. Of course, more generous schemes will cost more, and employee contributions may be higher than in a poorer scheme.

Examples of Accrual rate

• Bonds: Accrual rates for bonds are typically expressed as a percentage of the bond's face value. For example, a bond with a face value of $1,000 and an accrual rate of 5% would accrue $50 in interest each year.
• Mortgages: Accrual rates for mortgages vary depending on the loan term and the borrower's credit score. Generally, borrowers with higher credit scores will have access to lower accrual rates.
• Credit Cards: Credit cards typically have variable accrual rates, which are determined by the credit card issuer and can vary depending on the type of card and the cardholder's credit score.
• Loans: Loans typically have fixed accrual rates, which are determined by the lender and can vary depending on the term of the loan.
• Pensions: Pensions often have variable accrual rates, which may be determined by the pension plan or the pension provider. The rate is generally based on the performance of the pension funds and may be adjusted periodically.

Advantages of Accrual rate

Accrual rate is an important concept in finance that can have significant impacts on a wide variety of financial instruments. The advantages of setting an accrual rate include:

• Accrual rate helps to ensure that the financial instrument's interest rate remains consistent over time. This can help to protect the value of the instrument and ensure that lenders and borrowers alike can trust in the security of the instrument.
• Accrual rate can help to ensure that the interest rate does not become too high or too low. This helps to protect the instrument from volatile market conditions, which can make it difficult for lenders and borrowers to accurately predict the value of the instrument.
• Accrual rate can also help to provide a more accurate projection of the future value of the financial instrument. By setting an accrual rate, lenders and borrowers can accurately predict the future value of the instrument, allowing them to make more informed decisions regarding the instrument.
• Accrual rate also helps to protect the instrument from inflation. By setting an accrual rate, lenders and borrowers can ensure that the instrument's value remains consistent over time, regardless of changes in the market.

Limitations of Accrual rate

Accrual rate is a useful way to measure the return of financial instruments, but it does have some limitations. These limitations include:

• The rate does not take into account the effects of inflation, which can have a significant impact on the rate of return of an investment.
• Accrual rate does not include any expenses or commissions associated with the investment, which could have a significant impact on the overall return.
• Accrual rate also does not take into account the time-value of money, which can be important when evaluating long-term investments.
• The rate also does not take into account any taxes that might be owed on the investment, which can reduce the return.
• Finally, accrual rate does not consider the risk associated with any investment, which can also affect the return.

Other approaches related to Accrual rate

Accrual rate is an essential concept in the financial industry, and there are several other approaches related to it. These include:

• Amortization, which is the process of gradually paying off a debt with periodic payments over time.
• Compound interest, which is a type of interest in which the interest earned accumulates over time, increasing the total amount due.
• Discount rate, which is the rate of interest set by the Federal Reserve to influence market conditions and economic activity.
• Credit card APR, which is the cost of borrowing money expressed as an annual percentage rate.

In summary, accrual rate is an important concept in the financial industry, and there are several other related approaches including amortization, compound interest, discount rate, and credit card APR. Each of these approaches has its own unique implications and considerations.

Accrual rate — recommended articles

Net cost — Incremental borrowing rate — Plowback Ratio — Non-operating expense — Implicit interest rate — Annualized rate — Sinkable bond — Running yield — Net rate — Fish diagram

References

• Cox, J. C., Ingersoll Jr, J. E., & Ross, S. A. (2005). A theory of the term structure of interest rates. In Theory of Valuation (pp. 129-164).
• Jere R. Francis, Edward L. Maydew, and H. Charles Sparks (1999) The Role of Big 6 Auditors in the Credible Reporting of Accruals. Auditing: A Journal of Practice & Theory: September 1999, Vol. 18, No. 2, pp. 17-34.
• Patrick W. Thompson (1994) Images of rate and operational understanding of the fundamental theorem of calculus.Auditing: Educational Studies in Mathematics; March 1994, Volume 26, Issue 2-3, pp 229-274
• A.W. Stark (1989) Accounting and Economic Rates of Return: A Note On Depreciation and Other Accruals. Auditing: Journal of Business Finance & Accounting
• Michelle Hanlon (2005) Persistence and Pricing of Earnings, Accruals, and Cash Flows When Firms Have Large Book‐Tax Differences. The Accounting Review: January 2005, Vol. 80, No. 1, pp. 137-166.

Author: Krzysztof Kędys