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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:

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