Question

The rate of compound interest at which a sum of rs. 8000 amounts to rs. 8820 in 2 years, is:

Answer 1

Principal = Rs. 8000,  

Amount = Rs. 8820  

Let Rate % = R  

Time = 2 years  

By using formula,

=> 8820=8000(1+R/100)^2

=> 8820/8000=(1+R/100^)2

=> 441/400=(1+R/100)2

Taking square root of both sides,

=> 21/20=(1+R/100)

=> R = 5 %

Answer 2

The rate of compound interest at which a sum of rs. 8000 amounts to rs. 8820 in 2 years is 5%.

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Let's understand a few concepts:

To solve the given problem we will use the following formula of compound interest:

$\boxed{\bold{A = P \bigg(1+\frac{R}{100}\bigg)^n }}$

Where A = amount, P = principal, R = rate of compound interest and n = no. of years

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Let's solve the given problem:

The sum of money i.e., P = Rs. 8000

The amount received after 2 years i.e., A = Rs. 8820

The no. of years i.e., n = 2 years

Let "R" % be the rate of compound interest.

By substituting the given values in the above formula, we get

$8820 = 8000\bigg(1+\frac{R}{100}\bigg)^2$

$\implies \frac{8820}{8000} = \bigg(1+\frac{R}{100}\bigg)^2$

$\implies \frac{882}{800} = \bigg(1+\frac{R}{100}\bigg)^2$

$\implies \frac{441}{400} = \bigg(1+\frac{R}{100}\bigg)^2$

$\implies \bigg(\frac{21}{20}\bigg)^2 = \bigg(1+\frac{R}{100}\bigg)^2$

$\implies\frac{21}{20} = 1+\frac{R}{100}$

$\implies\frac{21}{20} - 1 =\frac{R}{100}$

$\implies\frac{21 - 20}{20} =\frac{R}{100}$

$\implies\frac{1}{20} =\frac{R}{100}$

$\implies R = \frac{100}{20}$

$\implies \bold{R = 5\%}$

Thus, the rate of compound interest is 5% p.a.

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