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.)