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## 3.6 Summary (EMCG8)

• Always keep the rate of interest per time unit and the time period in the same units.
• Simple interest: $$A = P(1 + in)$$
• Compound interest: $$A = P(1 + i)^n$$
• Simple depreciation: $$A = P(1 - in)$$
• Compound depreciation: $$A = P(1 - i)^n$$
• Nominal and effective annual interest rates: $$1 + i = \left( 1 + \frac{i^{(m)}}{m} \right)^{m}$$
• Future value of payments:

$F = \frac{x\left[(1 + i)^{n}-1\right]}{i}$

Payment amount:

$x = \frac{F \times i}{\left[(1 + i)^{n}-1\right]}$
• Present value of a series of payments:

$P = \frac{x \left[1 - (1 + i)^{-n} \right]}{i}$

Payment amount:

$x = \frac{P \times i}{\left[1 - (1 + i)^{-n}\right]}$