1.

If Rs.10,000 amounts to Rs.13,310 in 3 years at compound Interest,find the rate of interest.​

Answer»

Given:

  • Principal = Rs. 10000
  • Amount = Rs. 13,310
  • Time = 3 years

What To Find:

We have to find the rate (R) of the COMPUND INTEREST.

How To Find:

To find the rate, we will use,

\sf{A = P \bigg(1 + \dfrac{R}{100} \bigg)^T}

And subtitute the values and solve.

Solution:

Using the formula,

⇒ \sf{A = P \bigg(1 + \dfrac{R}{100} \bigg)^T}

Substitute the values,

⇒ \sf{13310 = 10000 \bigg(1 + \dfrac{R}{100} \bigg)^3}

Take 10000 to LHS,

⇒ \sf{ \dfrac{13310}{10000} = \bigg( 1 + \dfrac{R}{100} \bigg)^3

Take 100 as the LCM in the brackets,

⇒ \sf{ \dfrac{13310}{10000} = \bigg( \dfrac{100 + R}{100} \bigg)^3

Take the cube (3) to LHS,

⇒ \sf{\sqrt[3]{\dfrac{13310}{10000}} = \dfrac{100 + R}{100}}

Simplify 13310 by 10000,

⇒ \sf{\sqrt[3]{1.331} = \dfrac{100 + R}{100}}

Find the cube root of 1.331,

⇒ \sf{1.1 = \dfrac{100 + R}{100}}

Take 100 to LHS,

⇒ 1.1 × 100 = 100 + R

Multiply 1.1 by 100,

⇒ 110 = 100 + R

Take 100 to LHS,

⇒ 110 - 100 = R

Subtract 100 from 110,

⇒ 10 = R

∴ Thus, the rate of interest is 10 %.


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