Find CI when interest is compounded annually but Rates are different

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To find CI when interest is compounded annually but rates are different, we use the following formula :

A = P( 1 + R₁)( 1 + R₂)... ( 1 + R_n)

Where P = Principal
R ₁ ,R ₂ ,R ₃ ...interest rates percent for different years.

Examples :

1) Roger bought a refrigerator for $ 4000 on credit. The rate of interest for the first year is 5% and of the second year is 15%. How much will it cost him if he pays the amount after two years.

Solution:
Here, P = $ 4000, R ₁ = 5% p.a and R ₂ = 15% p.a.

∴ Amount after 2 years = P( 1 + R ₁ )( 1 + R ₂ )

= 4,000 x ( 1 + 0.05) ( 1 + 0.15)

= 4000 x ( 1.05) ( 1.15 )

= 4000 x 1.2075

= $ 4830
∴ The refrigerator will cost $ 4830 to Roger.
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2) Find the amount of $12,500 for 2 years compounded annually, the rate if interest being 15 % for the 1st year and 16 % for the second year.


Here, P = $12,500 , R₁ = 15 % and R₂ = 16 %

∴ Amount after 2 years = P( 1 + R₁)( 1 + R₂)

= 12,500x ( 1 + 0.15) ( 1 + 0.16)

= 12,500 x ( 1.15) ( 1.16 )

= 12,500 x 1.334

= $ 16,675
∴ Amount = $16,675

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Compound Interest(CI)

• Find Compound Interest when interest is compounded Half yearly
• Find Compound Interest when interest is compounded Quarterly
• Find CI when interest is compounded annually but Rates are different
• Finding Principal
• Finding Time Period of Investment
• Finding Rate of Interest

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