Question

A sum amounts to rs 18600 after 3 years and to 27900 after 6 years, at a certain rate percent p.A. When the interest compounded annually. The sum is

Answer 1

Answer:

principal P=Rs.9300

Rate of interest R =33 1/3%

Step-by-step explanation:

Answer 2

A sum amounts to rs 18600 after 3 years and to 27900 after 6 years, at a certain rate percent p.A. When the interest compounded annually. The sum is Rs 12400

Solution:

The formula for amount when compounded annually is given as:

$A=P\left(1+\frac{R}{100}\right)^{T}$

Where, P is the principal sum

R is the rate of interest

T is the number of years

Let the sum be Rs "x" and rate be "R"

Given that sum amounts to Rs 18600 after 3 years. Hence we frame equation as:

$x(1+\frac{R}{100})^{3}=18600$   ---- eqn 1

Also given that the sum amounts to Rs 27900 after 6 years. Hence the equation is:

$x(1+\frac{R}{100})^{6}=27900$    ---- eqn 2

Dividing eqn 2 by eqn 1 we get,

$\begin{array}{l}{\left(1+\frac{R}{100}\right)^{3}=\frac{27900}{18600}} \\\\ (1+\frac{R}{100})^{3}=\frac{3}{2}}\end{array}$

$\text { Substituting the value of }\left(1+\frac{R}{100}\right)^{3} \text { in Equation } 1$

$\begin{array}{l}{x(1+\frac{R}{100})^{3}=18600} \\\\ {x(\frac{3}{2})=186000} \\\\ {x=18600 \times \frac{2}{3}} \\\\ {x=12400}\end{array}$

Thus sum is Rs 12400

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