Time Value of Money

  • Value on money decreases by passage of terms
  • Money has 2 Values -> Present Value and Future Value
  • Formula for Future Value of Money (\(Future\ Value\ = \ P\ * (1+r)^n\)\) Where,
    • P -> Principal amount
    • r -> Rate of interest
    • n -> Time in Years

  • Present Value based on Future known value is given by, \(\(PV\ =\ FV\ * (\frac{1}{1+r})^n\ \ \ \ \ \ OR\ \ \ \ PV\ =\ FV\ * (1+r)^{-n}\)\) Where,

    • PV -> Present Value
    • FV -> Future Value
    • r -> Rate of interest
    • n -> Number of Years
    • The above two formulas equate to the same answer as \((1+r)^-n = (\frac{1}{1+r})^n\)

  • Future Value of Annuity \(\(FVAF\ = \ \frac{(1+r)^n - 1}{r}\)\)

    • FVAF -> Future Value Annuity Factor
    • C -> Cash Flow

  • Present Value of Annuity$$PVAF = \frac{1 - (1+r)^{-n}}{r} $$Where,

    • PVAF -> Present Value Annuity Factor

  • The above two values PVAF and FVAF are factors and are used in scenarios of Annuity.

  • When you are getting/paying the same amount for a fixed amount of years, this is called as Annuity
  • In cases where you have to pay a large given some in n years, and at x interest rate, do the following
    1. Calculate the PVAF/FVAF as needed
    2. Divide the large given sum by the calculated value
    3. The result you got is the amount you have to pay per year for n years.