# Summary

• 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,
• 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

• 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,

• Final amount in case of compound interest can be calculated in the following ways:
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• When interest is compounded annually but time is in fraction, say a  years, then

• When rates are different for different years, say R1%, R2%, R3% for 1st 2nd and 3rd year respectively, then;

• The effective rate of interest can be computed using the relation E = (1 + r)n â€“ 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
• For annuity due
• 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 .
• PV of an annuity regular can be calculated using the relation,
• 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