Question

Find the sum on which the difference between the simple interest and the compound interest at the rate of 8% per annum compounded annually be ₹64 in 2 years.
Tell the answer by taking sum as ₹100.​

Answer 1

Correct Question

Find the sum on which the difference between the simple interest and the compound interest at the rate of 8% per annum compounded annually be ₹64 in 2 years.

Answer

Given :

Difference : ₹64

Rate of interest : 8%

Time : 2 years

To find :

The sum invested at the bank.

Solution :

First, we'll find the simple interest.

Simple interest :

$\sf \dashrightarrow SI = \dfrac{P \times R \times T}{100}$

$\sf \dashrightarrow \dfrac{P \times 8 \times 2}{100}$

$\sf \dashrightarrow \dfrac{P \times 16}{100}$

$\sf \dashrightarrow \dfrac{16P}{100} = \dfrac{4P}{25}$

Now, let's find the compound interest.

Compound interest :

$\sf \dashrightarrow Amount = Principle \bigg( 1 + \dfrac{Rate}{100} \bigg)^{Time}$

$\sf \dashrightarrow P \bigg( 1 + \dfrac{8}{100} \bigg)^{2}$

$\sf \dashrightarrow P \bigg( 1 + \dfrac{2}{25} \bigg)^{2}$

$\sf \dashrightarrow P \bigg( \dfrac{25 + 2}{25} \bigg)^{2}$

$\sf \dashrightarrow P \bigg( \dfrac{27}{25} \bigg)^{2}$

$\sf \dashrightarrow P \bigg( \dfrac{729}{625}$

$\sf \dashrightarrow \dfrac{729P}{625}$

Now, let's find the principle value.

Principle (sum) :

$\sf \dashrightarrow Difference = CI - SI$

$\sf \dashrightarrow 64 = \dfrac{729P}{625} - \dfrac{4P}{25}$

$\sf \dashrightarrow 64 = \dfrac{729P - 100P}{625}$

$\sf \dashrightarrow 64 = \dfrac{639P}{625}$

$\sf \dashrightarrow 639P = 64(625)$

$\sf \dashrightarrow 639P = 40000$

$\sf \dashrightarrow P = \dfrac{40000}{639}$

$\sf \dashrightarrow P = 62.59$

Hence, the principle (sum) amount is ₹62.59.