Question

Principal=₹20000
Compound interest (after 2 years=₹3328

Find the rate of intrest

Answer 1

Given:

Principal = ₹ 20000

Time period = 2 years

Compound Interest = ₹ 3328

To find:

The rate of interest

Solution:

Let "R%" represent the rate of interest.

The formula to calculate the compound interest is as follows:

$\boxed{\boxed{\bold{Compound \:Interest = P[(1 + \frac{R}{100})^n -1 ]}}}$

where

P = Principal

R = rate of interest

n = no. of years

Now, substituting the given values in the formula,

$3328 = 20000[(1 + \frac{R}{100})^2 -1 ]$

$\implies \frac{3328}{20000} = (1 + \frac{R}{100})^2 -1$

$\implies 0.1664 = (1 + \frac{R}{100})^2 -1$

$\implies 0.1664 + 1 = (1 + \frac{R}{100})^2$

$\implies 1.1664 = (1 + \frac{R}{100})^2$

taking square root on both sides

$\implies \sqrt{1.1664 } = \sqrt{(1 + \frac{R}{100})^2}$

$\implies 1.08 = 1 + \frac{R}{100}$

$\implies 1.08 - 1 = \frac{R}{100}$

$\implies 0.08 = \frac{R}{100}$

$\implies R = 0.08 \times 100$

$\implies \bold{ R = 8\%}$

Thus, the rate of interest is 8%.

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