Question

If the amount bf Rs. 400/- for 2 years is 441 then find the annual rate of compound interest
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Answer 1

Given:

Principal (P) = Rs. 400

Time (n) = 2 years

Amount (A) = Rs. 441

To be found:

The rate of interest compounded annually.

Rate of interest (R%) =?

Now,

$\underline{\sf{Formula\ for\ finding\ Amount(A)}}$

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

So,

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

[Putting the given values of 'P', 'A' and 'n']

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

[Taking 400 to LHS]

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

$\implies \sqrt{\frac{441}{400}} = 1+\frac{R}{100}$

[Taking square root in both the sides]

$\implies \frac{\sqrt{441}}{\sqrt{400}} = 1+\frac{R}{100}$

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

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

[Taking 1 to LHS, which becomes (-1) ]

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

[ Taking LCM = 20 ]

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

$\implies 20 \times R = 1 \times 100$

$\implies R = \frac{10\not0}{2\not0}$

[Taking 20 to RHS]

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

Hence,

The Rate of Interest compounded annually is 5% p.a

Answer 2

We can find the rate of interest by using the Formula for finding amount.

=> A = P[1 + R/100]^T

Given P = 400

A = 441

T = 2 years

Put all the given values in the formula

441 = 400[1 + R/100]^2

=> 441/400 = [1 + R/100]^2

=> 21/20 = 1 + R/100

=> 21/20 - 1 = R/100

=> 1/20 = R/100

=> R = 5%

Hence, R% = 5%