# Accrual rate

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**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:

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:

## 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.

## 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