2. Compound interest : Derivation for amount from the
equation of simple interest
3. In some cases, the interest is added to the principal to
form a new principal ,which maybe reinvested for
the next time period. The difference between the
original principal and the amount at the end of the
last time period is known as compound interest.
4. Letβs see how we can compute the total amount.
Let
P be the principal
r be the rate of interest
n be the number of years
5. We have
I=( Pnr)/ 100
Interest for the first year
I1 =Px r /100
A1 = P + (Pr/100)
= P(1+(r/100))
6. Principal for the second year = P+( P x r/100)
=P(1+ (r/100))
Interest = P(1+ (r/100))x(r/100)
A2 = P(1 + (r/100)) + P ( 1+ (r/100)) x (r/100 )
= P (1 + r/100) 2
7. Principal for the third year = P (1+ (r/100)) 2
Interest = P (1 + (r/100)) 2 x (r/100)
A3 = P (1 + (r/100 )) 2 + P (1 +(r/100)) 2 x (r/100)
= P (1 +(r/100)) 2 x ( 1+(r/100 ))
= P(1 + ( r/100 )) 3
8. Continuing like this , the amount A , including
after n years is given by
A= P (1+(r/100)) n
9. Amount = P(1 +(r /100 )) n
Where
P= Principal amount
r = rate of interest
n = number of years
