Question

simple interest and compound interest on rs.100000 at 10%pcpa for 5 yrs​

Answer 1

Given :

Principle : ₹100000

Rate of interest : 10%

Time : 5 years

To find :

The simple interest and the compound interest.

Solution :

First we'll find the simple interest.

Simple interest :

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

$\sf \dashrightarrow \dfrac{100000 \times 10 \times 5}{100}$

$\sf \dashrightarrow \dfrac{100000 \times 1 \times 5}{10}$

$\sf \dashrightarrow \dfrac{100000 \times 5}{10}$

$\sf \dashrightarrow \dfrac{100000 \times 1}{2}$

$\sf \dashrightarrow \cancel \dfrac{100000}{2} = 50000$

Now, let's find the amount when the principle is compounded.

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

$\sf \dashrightarrow 100000 \bigg( 1 + \dfrac{10}{100} \bigg)^{5}$

$\sf \dashrightarrow 100000 \bigg( \dfrac{100 + 10}{100} \bigg)^{5}$

$\sf \dashrightarrow 100000 \bigg( \dfrac{110}{100} \bigg)^{5}$

$\sf \dashrightarrow 100000 \bigg( \dfrac{11}{10} \bigg)^{5}$

$\sf \dashrightarrow 100000 \bigg( \dfrac{11^5}{10^5} \bigg)$

$\sf \dashrightarrow 100000 \bigg( \dfrac{161051}{100000} \bigg)$

$\sf \dashrightarrow \dfrac{100000 \times 161051}{100000} = \dfrac{16105100000}{100000}$

$\sf \dashrightarrow \cancel \dfrac{16105100000}{100000} = 161051$

Now, let's find the compound interest.

Compound interest :

$\sf \dashrightarrow Amount - Principle$

$\sf \dashrightarrow 161051 - 100000$

$\sf \dashrightarrow Rs.61051$

Hence, the simple interest and compound interest are ₹50000 and ₹61051 respectively.