Question

On a certain sum of money, after 2 years the simple interest and compound interest obtained are rs 400 and rs 600 respectively. What is the sum of money invested?

Answer 1

Given:

On a certain sum of money, after 2 years the simple interest and compound interest obtained are ₹ 400 and ₹ 600 respectively.

To Find:

What is the sum of money invested?

Solution:

here, given that simple interest and compound interest obtained are ₹ 400 and ₹ 600 respectively in 2 years.

therefore, S.I.= 400 , C.I.=600 , T=2 and n = 1

since, we know , simple interest is given by

$\[S.I = \dfrac{{P \times R \times T}}{{100}}\]$

$\[\begin{gathered} 400 = \frac{{P \times R \times 2}}{{100}} \hfill \\ R = \frac{{20000}}{P} \hfill \\ \end{gathered} \]$     ----(1)

Compound interest is given by

$\[C.I = P{\left( {1 + \frac{R}{n}} \right)^{nT}} - P\]$

therefore,

$600 = P{\left( {1 + \frac{R}{1}} \right)^{1 \times 2}} - P \hfill \\ \\ 600 = P[{(1 + R)^2} - 1] \hfill$

On substituting value of R from equation (1) is ;

$\[\begin{gathered} 600 = P\left[ {{{\left( {1 + \frac{{20000}}{P}} \right)}^2} - 1} \right] \hfill \\ 600 = P\left[ {\frac{{{P^2} + 4 \times {{10}^8} + 2 \times P \times 2 \times {{10}^4}}}{{{P^2}}} - 1} \right] \hfill \\ 600P = 4 \times {10^8} + 40000P \hfill \\ 39400P = - 4 \times {10^8} \hfill \\ P = 10152.28 \hfill \\ \end{gathered} \]$

Hence, ₹ 10152.28 is the sum of money invested.

Answer 2

Given :- On a certain sum of money, after 2 years the simple interest and compound interest obtained are rs 400 and rs 600 respectively. What is the sum of money invested ?

Solution :-

we know that,

• Simple interest is same in every year.
• compound interest and simple interest are same in first year.

with these two statement, we can solve this question very easily .

given now,

• Time = 2 years.
• Simple interest received = 400 => 200 each year.
• compound interest = 600 => 200 in first year as equal to Simple interest and than 400 in second year.

So,

→ Extra compound interest = 400 - 200 = Rs.200 .

Than,

→ Rate of interest = (200 * 100) / 200 = 100% . { in CI we gets interest on interest , which is equal to rate %.}

Therefore,

→ Simple interest = (Principal * Rate * Time) / 100

→ 200(1 year) = (Principal * 100 * 1) / 100

→ 100 * Principal = 200 * 100

dividing both sides by 100,

→ Principal = Rs.200 (Ans.)

Hence, The sum of Money invested is Rs.200 and Rate of interest is 100% per annum.

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