Simple Interest and Compound Interest

SIMPLE INTEREST

1. Principal: The money borrowed or lent out for a certain period is called the principal or the sum.

2. Interest: Extra money paid for using other's money is called interest.

3. Simple Interest (S.I.) : If the interest on a sum borrowed for a certain period is reckoned uniformly, then it is called simple interest.

Let Principal = P, Rate = R% per annum (p.a.) and Time = T years. Then,

  (i)         S.I. =  (P*R*T )/100

  (ii)        P=(100*S.I)/(R*T) ;R=(100*S.I)/(P*T) and T=(100*S.I)/(P*R)

COMPOUND INTEREST

Compound Interest: Sometimes it so happens that the borrower and the lender agree to fix up a certain unit of time, say yearly or half-yearly or quarterly to settle the previous account.

        In such cases, the amount after first unit of time becomes the principal for the second unit, the amount after second unit becomes the principal for the third unit and so on.

After a specified period, the difference between the amount and the money borrowed is called the Compound Interest (abbreviated as C.I.) for that period.

                                                        

Let Principal = P, Rate = R% per annum, Time = n years.

I. When interest is compound annually:

                                    Amount = P(1+R/100)ⁿ

II. When interest is compounded Half-yearly:

                                    Amount = P[1+(R/2)/100]²ⁿ­

             

            III. When interest is compounded quarterly:  

                                                Amount = P[ 1+(R/4)/100]⁴ⁿ­

IV. When interest is compounded AnnuaI1y but time is in fraction, say 3(2/5) years.

Amount = P(1+R/100)³ x (1+(2R/5)/100)

V. When Rates are different for different years, say Rl%, R2%, R3% for 1st, 2nd and 3rd year respectively.

Amount = P(1+R₁/100)(1+R₂/100)(1+R₃/100)

          VI. Present worth of Rs.x due n years hence is given by :

Present Worth = x/(1+(R/100))ⁿ