Discrete end-of-period compound-interest factors, a generated factor table for common rates, the MACRS depreciation rate schedules, and learning-curve rates and factors.
Compound-Interest Factor Formulas
i = interest rate per period, n = number of periods. Standard notation: (X/Y, i, n) means "find X given Y".
| Factor | Notation | Formula | Finds |
|---|---|---|---|
| Single-payment compound amount | (F/P, i, n) | (1 + i)n | Future worth of a present sum |
| Single-payment present worth | (P/F, i, n) | 1(1 + i)n | Present worth of a future sum |
| Uniform-series compound amount | (F/A, i, n) | (1 + i)n − 1i | Future worth of a uniform series |
| Sinking fund | (A/F, i, n) | i(1 + i)n − 1 | Uniform series to reach a future sum |
| Uniform-series present worth | (P/A, i, n) | (1 + i)n − 1i (1 + i)n | Present worth of a uniform series |
| Capital recovery | (A/P, i, n) | i (1 + i)n(1 + i)n − 1 | Uniform series to recover a present sum |
| Arithmetic-gradient uniform series | (A/G, i, n) | 1i − n(1 + i)n − 1 | Equivalent uniform series of a gradient |
| Arithmetic-gradient present worth | (P/G, i, n) | (1 + i)n − i n − 1i2 (1 + i)n | Present worth of a gradient |
- r
- Nominal rate per period
- m
- Compounding periods per period
- ieff
- Effective rate
- n
- Periods for money to double
ieff = ( 1 + rm )m − 1
ieff = er − 1 (continuous)
n ≈ 72100 i (rule of 72)
Interest Factor Table
| n | (F/P) | (P/F) | (A/P) | (P/A) | (F/A) | (A/F) |
|---|
MACRS GDS Depreciation Rates (% of basis)
| Year | 3-yr | 5-yr | 7-yr | 10-yr | 15-yr | 20-yr |
|---|---|---|---|---|---|---|
| 1 | 33.33 | 20.00 | 14.29 | 10.00 | 5.00 | 3.75 |
| 2 | 44.45 | 32.00 | 24.49 | 18.00 | 9.50 | 7.22 |
| 3 | 14.81 | 19.20 | 17.49 | 14.40 | 8.55 | 6.68 |
| 4 | 7.41 | 11.52 | 12.49 | 11.52 | 7.70 | 6.18 |
| 5 | — | 11.52 | 8.93 | 9.22 | 6.93 | 5.71 |
| 6 | — | 5.76 | 8.92 | 7.37 | 6.23 | 5.29 |
| 7 | — | — | 8.93 | 6.55 | 5.90 | 4.89 |
| 8 | — | — | 4.46 | 6.55 | 5.90 | 4.52 |
| 9 | — | — | — | 6.56 | 5.91 | 4.46 |
| 10 | — | — | — | 6.55 | 5.90 | 4.46 |
| 11 | — | — | — | 3.28 | 5.91 | 4.46 |
| 12 | — | — | — | — | 5.90 | 4.46 |
| 13 | — | — | — | — | 5.91 | 4.46 |
| 14 | — | — | — | — | 5.90 | 4.46 |
| 15 | — | — | — | — | 5.91 | 4.46 |
| 16 | — | — | — | — | 2.95 | 4.46 |
| 17 | — | — | — | — | — | 4.46 |
| 18 | — | — | — | — | — | 4.46 |
| 19 | — | — | — | — | — | 4.46 |
| 20 | — | — | — | — | — | 4.46 |
| 21 | — | — | — | — | — | 2.23 |
3-, 5-, 7- and 10-year classes use 200% declining balance switching to straight-line; 15- and 20-year classes use 150% declining balance. The half-year convention treats all property as placed in service at the mid-point of the first year, so the schedule runs one year longer than the class life.
Learning Curve Factors
| Industry or operation | Typical rate | Calculator preset |
|---|
The factors follow the unit-time model of the Learning Curve calculator [5]: multiply by the first-unit time T1.