Question

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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Answer 1

Answer:

Required rate of interest is 8%.

Step-by-step explanation:

Let the principal be Rs P and rate of interest be R% p.a.

$\boxed{\mathsf{ Simple\:Interest =\dfrac{Principal \times Rate \times Time}{100}}}\\\\\boxed{\mathsf{Compound\:Interest=P\bigg[ \bigg( 1+\dfrac{r}{100} \bigg)^n - 1 \bigg] }}$

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%.

Answer 2

Step-by-step explanation:

by 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

4,1