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  • The simple interest on a given principal P, for a time period T and at a rate of interest R% is calculated using the relation, Description: 58187.png
  • Final amount A is the sum of the principal P and the simple interest, i.e.A = P + S.I.
  • When we know the amount accumulated on a principal after two different time periods, we can find the rate of interest using the relation
    Description: 58207.png 
  • If two different principals are lent out at two different rates of interest, then the rate of interest on the overall principal is calculated using the relation,
    Description: 58227.png 
  • Final amount in case of compound interest can be calculated in the following ways:
    • ƒ Description: 58253.png 
    • ƒ Description: 58268.png 
    • Description: 58279.png
    • When interest is compounded annually but time is in fraction, say a Description: 58286.png years, then
      Description: 58298.png 
    • When rates are different for different years, say R1%, R2%, R3% for 1st 2nd and 3rd year respectively, then;
      Description: 58305.png 
  • The effective rate of interest can be computed using the relation E = (1 + r)n – 1
  • To be called an annuity, a series of payments (or receipts) must have the following features:
  1. Amount paid (or received) must be constant over the period of annuity
  2. Time interval between two consecutive payments (or receipts) must be the same
  • Types of Annuity:
    • Annuity Regular: first payment/receipt takes place at the end of first period
    • Annuity Due or Annuity Immediate: first receipt or payment is made at the beginning of the annuity
  • Future value of a single cash flow can be computed using the relation FV = CF (1 + r)n
  • Future value of an annuity regular is given by Description: 58496.png
  • For annuity due Description: 58557.png
  • Present value (PV) of an amount A due at the end of n interest periods at a rate of interest r (in decimals) can be obtained by Description: 58563.png.
  • PV of an annuity regular can be calculated using the relation,Description: 58572.png
  • For annuity due, first find the PV using the above formula for a time period 1 less than the given time period. To this value, add the initial payment.
  • Size of a sinking fund is computed using the relation Description: 58578.png

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