Question

At what rate% per annum compound interest will 2209 amount to 2601 in two years​

Answer 1

Given:

At what rate% per annum compound interest will 2209 amount to 2601 in two years​?

To find:

The rate% per annum compound interest

Solution:

The sum of money, P = Rs. 2209

The no. of years, n = 2 years

The amount after 2 years, A = Rs. 2601

Let "R %" be the rate of interest.

We know,

$\boxed{\bold{A = P [1 + \frac{R}{100} ]^n}}$

Now, on substituting the given values of A, P and n in the formula above, we get

$2601= 2209 [1 + \frac{R}{100} ]^2}}$

$\implies 2601= 2209 [1 + \frac{R}{100} ]^2}}$

$\implies \frac{2601}{2209} = [1 + \frac{R}{100} ]^2}}$

taking square roots on both the sides

$\implies \sqrt{ \frac{2601}{2209}} = \sqrt{[1 + \frac{R}{100} ]^2}}}$

$\implies \frac{51}{47}} = 1 + \frac{R}{100}$

$\implies \frac{51}{47}} - 1 = \frac{R}{100}$

$\implies \frac{51 -47}{47}} = \frac{R}{100}$

$\implies \frac{4}{47}} = \frac{R}{100}$

$\implies R = \frac{400}{47}}$

$\implies \bold{R =8.5\%}$

Thus, 8.5 % per annum compound interest will 2209 amount to 2601 in two years​.

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