What is the rate of interest in if simple interest earned on a certain sum for the 3rd year is Rs 2 ...........

Quantitative Aptitude (CGL) Compound Interest

What is the rate of interest (in %) if simple interest earned on a certain sum for the 3rd year is Rs 2,000 and compound interest earned in 2 years is Rs 4,160?

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Explanation:

According to the question :
= > Simple interest for 3rd year = Rs 2,000
= > ( P x R x T ) / 100 = Rs 2,000
= > P x R x 1 = Rs 2,000 x 100
= > P = Rs 2,00,000 / R ... ( 1 )
= > Compound interest for 2 years = Rs 4,160
= > P[ ( 1 + R / 100 )^2 - 1 ] = Rs 4,160
= > P[ 1 + R² / 10000 + R / 50 - 1 ] Rs 4,160
= > P[ R² / 10000 + R / 50 ] = Rs 4,160
Substituting the value of P from ( 1 )
= > Rs ( 200000 / R )[ R² / 10000 + R / 50 ] = Rs 4,160
= > ( 200000 / R ) x R[ R / 10000 + 1 / 50 ] = 4160
= > 200000( R / 10000 + 1 / 50 ) = 4160
= > 20R + 4000 = 4160
= > 20R = 160
= > R = 8
Hence the required rate of interest is 8%