BIZOMAT MAKEOS · Money
Interest and Equivalence Factors
What are the compound interest factors for this rate and period?
Single-payment, uniform-series and gradient compound interest factors (F/P, P/F, A/P, P/A, A/F, F/A, A/G, P/G) and the effective annual rate for a nominal rate and compounding frequency.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Nominal annual rate | % | Nominal annual interest or discount rate. |
| Number of periods (years) | years | Number of years. |
| Compounding periods per year | per year | Compounding frequency (1 annual, 12 monthly). |
| Amount to convert | AUD | An amount used to illustrate each factor. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Nominal annual rate
- What it is
- The stated yearly interest or discount rate before allowing for compounding more than once a year.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0% to 200%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 8% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher rate raises future-value factors and lowers present-value factors.
- Get it right
- Type the percentage itself. With monthly compounding the effective rate is higher than this.
What this means: Number of periods (years)
- What it is
- The number of years over which money is moved forward or back in time.
- Units and format
- Enter a number in years: years. The form accepts 1 years to 200 years. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 years as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More years widen the gap between present and future values.
- Get it right
- Enter years; the compounding frequency is set separately.
What this means: Compounding periods per year
- What it is
- How many times a year interest is added to the balance, for example once a year or every month.
- Units and format
- Enter a number in per year: per year. The form accepts 1 per year to 365 per year. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 per year as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More frequent compounding raises the effective annual rate.
- Get it right
- Use the compounding frequency of the loan or account, not the payment frequency.
What this means: Amount to convert
- What it is
- An amount of money that each factor is applied to in the results table, to show what it means in dollars.
- Units and format
- Enter a number in AUD: Australian dollars. The form accepts 0 AUD or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10000 AUD as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only scales the illustrative amounts in the table.
- Get it right
- It does not change the factors themselves, only the illustrative column.
Method and formulas
- Effective annual rate i = (1 + r/m)^m − 1.
- F/P = (1 + i)ⁿ; P/A = ((1 + i)ⁿ − 1) ÷ (i(1 + i)ⁿ); A/F = i ÷ ((1 + i)ⁿ − 1); others are reciprocals.
- A/G = 1/i − n ÷ ((1 + i)ⁿ − 1); P/G = (P/A − n(1 + i)^−n) ÷ i.
- Example: at 8% over 10 years, P/A = 6.7101 and A/P = 0.14903.
Limitations
- End-of-period cash flows; beginning-of-period (annuity due) amounts are larger by (1 + i).
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Convert between present, future and annual amounts
- Check engineering economics calculations
- Convert a nominal rate to an effective rate
Who it is for
- Engineering managers
- Project engineers
- Finance and business analysts
What you get
- Effective annual rate
- Table of interest factors and converted amounts
Interpreting the result
- Multiply a known amount by the factor for the conversion you need (e.g. P × A/P = equivalent annual amount).
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 134–139. Topic reference; no source tables or recommended settings are reproduced.
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