# 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:
- Âƒ
- Âƒ
- When interest is compounded annually but time is in fraction, say
*a years, then* - When rates are different for different years, say
*R*_{1}%,*R*_{2}%,*R*_{3}% for 1st 2nd and 3rd year respectively, then;

- The effective rate of interest can be computed using the relation
*E*= (1 +*r*)â€“ 1^{n} - To be called an annuity, a series of payments (or receipts) must have the following features:

- Amount paid (or received) must be constant over the period of annuity
- 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