16.3: Rounding Rules

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Jean-Paul Olivier
Red River College of Applied Arts, Science, & Technology

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Global Textbook Rounding Rules

All interim solutions never get rounded unless there is a logical reason or business process that forces the number to be rounded.
When writing non-terminating decimals in this textbook, only the first six (or up to six) decimals are written. The horizontal line format is used for repeating decimals. If the number is not a final solution, then it is assumed that all decimals or as many as possible are being carried forward.
All final numbers are rounded to six decimals in decimal format, and four decimals in percentage format unless instructions indicate otherwise.
Final solutions are rounded according to common business practices, practical limitations, or specific instructions.
Zeroes not required at the end of decimals are generally not written unless required to meet a rounding standard or to visually line-up a sequence of numbers.

Topic-Specific Rounding Rules

Section 4.1, Gross Earnings, Salaries: When calculating overtime pay, maintain all decimals in the hourly rate and only round the final pay amount.

Section 4.3, Indexes, Index Numbers: Index numbers with a 100 base are rounded to one decimal. If the index number represents dollars, then a two decimal standard is used. All other indexes require a specific rounding instruction.

Section 5.2, Break-Even Analysis, Break-even Units: All break-even units are always rounded upwards to the next integer regardless of the actual value of the decimal.

Section 7.1, Sales Taxes: The calculation of any sales tax amount is rounded to two decimals.

Section 7.2: Property Taxes: Mill rates are commonly expressed in four decimals and tax rates are commonly expressed in six decimals.

Section 7.3: Exchange Rates: In true markets, exchange rates are commonly expressed with ten decimals or more. A four decimal standard is used for mathematical purposes in this book.

Section 8.5: Demand Loan Repayment Schedules: For simplicity when writing the numbers into repayment schedules and performing all calculations, round all interest calculations to two decimals throughout the table.

Chapter 9 onwards: The calculated value of the periodic interest rate is never rounded in any interim calculation.

Section 9.5, Determining The Interest Rate, Calculating IY: Due to an imprecise single payment used in the calculation, IY is rounded to an integer or early decimal position only if it has a marginal effect. If unable to produce a marginal effect, round as per global rounding rules.

Section 9.7, Determining The Number Of Compounds, Calculating N: Due to an imprecise single payment used in the calculation, N is rounded to the nearest integer if it would be the same result as rounding to three decimals. If rounding to three decimals is not equal to rounding to an integer, then all decimals must be carried forward in further calculations.

Section 9.7, Determining The Number Of Compounds, Calculating Days: Any calculation of days is always rounded to the nearest integer since interest can only be compounded daily at minimum.

Section 10.3, Savings Bonds, Regular Interest Savings Bond Interest Payments: Each interim interest payment must be rounded to two decimals.

Section 11.5, Number Of Annuity Payments, Calculating N: N is rounded to the nearest integer if it would be the same result as rounding to three decimals. If rounding to three decimals is not equal to rounding to an integer, then N is always rounded up to the next nearest integer regardless of the actual value of the decimal.

Section 11.6, Annuities Interest Rates, Calculating IY: Similar to Section 9.5, due to imprecise variable(s) used in the calculation IY is rounded to an integer or early decimal position only if it has a marginal effect. If unable to produce a marginal effect, round as per global rounding rules.

Section 12.1, Deferred Annuities, Moving Money Between Accumulation and Payment Stages: Money is commonly transferred between bank accounts between the two stages requiring the interim amount to be rounded to two decimals.

Section 13.3, Amortization Schedules: When writing amounts in the table, round the answers to two decimals. However, behind the scenes all calculations must be unrounded.

Section 14.1, Bond Coupon Payment Amount: The variable PMT_BOND must be unrounded throughout all calculations.

Section 14.1, Bond Cash Price On A Non-Interest Date: Formula 14.5 must use the unrounded value of the Date Price in its calculation.

Section 14.3, Sinking Fund Schedules: When writing amounts in the table, round the answers to two decimals. However, behind the scenes all calculations must be unrounded.

Section 15.1, Net Present Value: Due to the imprecision of future cost and profit estimates, the net present value is rounded off to the nearest dollar unless otherwise specified.

Section 15.1, Net Present Value Ratio: When performing this calculation in hard capital rationing, it is round this variable to two decimals.