# CLASS-9COMPOUND INTEREST FOR DIFFERENT RATES & YEARS USING FORMULAE

Finding Compound Interest When Rates Are Different for Different Years -

Let the rates of interest for three successive years be R₁%, R₂%, and R₃% per annum respectively. Then,

R₁              R₂               R₃

Amount = \$ { P ( 1 + ------ ) ( 1 + ------ ) ( 1 + ------ )}

100             100             100

Example.1) How much will \$ 10000 amount to in 2 years at compound interest, compounded annually, the rates of interest for the successive years being 8% and 10% respectively ?

Ans.) Given, P = \$ 10000, R₁ = 8% p.a, and R₂ = 10% p.a

As per the formula,

R₁                R₂

Amount = \$ { P ( 1 + ------- ) ( 1 + ------- ) }

100              100

8               10

= \$ { 10000 X ( 1 + ------ ) ( 1 + ------ ) }

100             100

2                1

= \$ { 10000 X ( 1 + ------ ) ( 1 + ------ ) }

25               10

2                1

= \$ { 10000 X  ( 1 + ------ ) ( 1 + ------ ) }

25               10

27         11

= \$ ( 10000 X ------ X ------ )

25         10

=  \$ ( 40 X 27 X 11 ) =  \$ 11880

Hence amount after 2 years will be \$ 11880         (Ans.)