Question

The CI on a certain sum at 10% pa for 2yrs is Rs.6548. What is SI on the sum of money at 7% pa for 4 years (approx)?

Answer 1

Given :

Compound interest : ₹6548

Rate of interest : 10%

Time : 2 years

To find :

The simple interest at sand principle and 7% per annum for 4 years.

Solution :

First, w should find the principle value by the formula of compound interest.

$\sf \dashrightarrow CI = P \bigg( 1 + \dfrac{R}{100} \bigg)^{T} - P$

$\sf \dashrightarrow 6548 = P \bigg( 1 + \dfrac{10}{100} \bigg)^{2} - P$

$\sf \dashrightarrow 6548 = P \bigg( \dfrac{100 + 10}{100} \bigg)^{2} - P$

$\sf \dashrightarrow 6548 = P \bigg( \dfrac{110}{100} \bigg)^{2} - P$

$\sf \dashrightarrow 6548 = P \bigg( \dfrac{11}{10} \bigg)^{2} - P$

$\sf \dashrightarrow 6548 = P \bigg( \dfrac{11^2}{10^2} \bigg) - P$

$\sf \dashrightarrow 6548 = P \bigg( \dfrac{121}{100} \bigg) - P$

$\sf \dashrightarrow 6548 = \dfrac{121P}{100} - P$

$\sf \dashrightarrow 6548 = \dfrac{121P - 100P}{100}$

$\sf \dashrightarrow 6548 = \dfrac{21P}{100}$

$\sf \dashrightarrow 21P = 6548 \times 100$

$\sf \dashrightarrow 21P = 654800$

$\sf \dashrightarrow P = \dfrac{654800}{21}$

$\sf \dashrightarrow P = 31180.95$

Now, we can find the simple interest.

Simple interest :

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

$\sf \dashrightarrow \dfrac{31180.95 \times 7 \times 4}{100}$

$\sf \dashrightarrow \dfrac{31180.95 \times 7 \times 1}{25}$

$\sf \dashrightarrow \dfrac{3118095 \times 7}{2500}$

$\sf \dashrightarrow \dfrac{623619 \times 7}{500}$

$\sf \dashrightarrow \cancel \dfrac{4365333}{500} = 8730.666$

Hence, the simple interest is ₹8730.666.