Question

(iii) Ritu gets 760 simple interest on a sum of money for 2
years at 5% per annum, how much compound interest she
will get on the same rate for the same time?
​

Answer 1

Answer :-

• The compound interest is Rs 779.

To find :-

• The compound interest.

Solution :-

• Before finding the compound interest, we have to find the principal using the simple interest, rate and time.

We know that :-

$\underline{ \boxed{\sf SI = \dfrac{Principal \times Rate \times Time}{100}}}$

Where,

• SI = Simple Interest.

Here,

• Simple interest = Rs 760.
• Rate = 5% per annum.
• Time = 2 years.

• Let the principal be "p".

Substituting the given values in this formula,

$\longmapsto \tt760 = \dfrac{p \times 5 \times 2}{100}$

$\longmapsto\tt760 = \dfrac{p \times 10}{100}$

$\longmapsto\tt760 = \dfrac{10p}{100}$

$\longmapsto \tt760 \times 100 = 10p$

$\longmapsto\tt76000 = 10p$

$\longmapsto\tt\dfrac{76000}{10} = p$

$\longmapsto\overline{ \boxed{ \tt Rs \: 7600 = p}}$

------------------------------------

• Now, as we know the principal, let's find the compound interest! For that, let's first find the amount.

We know that :-

$\underline{ \boxed{\sf Amount = Principal \left(1 + \dfrac{Rate}{100}\right)^{Time}}}$

Here,

• Principal = Rs 7600.
• Rate = 5% per annum.
• Time = 2 years.

Therefore,

$\longmapsto\rm Amount = 7600 \left(1 + \dfrac{5}{100} \right)^{2}$

$\longmapsto\rm Amount = 7600 \left(1 + \dfrac{1}{20} \right)^{2}$

$\longmapsto\rm Amount = 7600 \left( \dfrac{1 \times 20 + 1 \times 1}{20} \right)^{2}$

$\longmapsto\rm Amount = 7600\left( \dfrac{20 + 1}{20} \right)^{2}$

$\longmapsto \rm Amount = 7600\left(\dfrac{21}{20} \right)^{2}$

$\longmapsto\rm Amount = 7600 \times \dfrac{21}{20} \times \dfrac{21}{20}$

$\longmapsto\rm Amount = 7600 \times \dfrac{441}{400}$

$\longmapsto\rm Amount = 76 \!\!\!\not0 \!\!\!\not0 \times \dfrac{441}{4 \!\!\!\not0 \!\!\!\not0}$

$\longmapsto\rm Amount = 76 \times \dfrac{441}{4}$

$\longmapsto\rm Amount = \dfrac{33516}{4}$

$\longmapsto\overline{ \boxed{ \rm Amount = Rs \: 8379}}$

------------------------------------

• Finally, let's find the compound interest!

We know that :-

$\underline{ \boxed{\sf CI = Amount - Principal}}$

Where,

• CI = Compound Interest.

Here,

• Amount = Rs 8379.
• Principal = Rs 7600.

Hence,

$\boxed{ \bf CI = 8379 - 7600}$

$\boxed{\bf CI = Rs \: 779}$

________________________________

• Hence, the compound interest Ritu will get on the same rate for the same time is Rs 779.