Question

Find the amount and the compound interest on ₹5000 at 10% p.a. for 1 year compound interest reckoned semi-annually.​

Answer 1

Given :

Principle : ₹5000

Rate of interest : 10%

Time : 1 year

To find :

The compound interest if the amount is reckoned semi-annually.

Solution :

First, we should find the amount.

$\sf \dashrightarrow Amount = Principle \bigg( 1 + \dfrac{Rate}{2 \times 100} \bigg)^{Time(2)}$

$\sf \dashrightarrow 5000 \bigg( 1 + \dfrac{10}{2 \times 100} \bigg)^{1(2)}$

$\sf \dashrightarrow 5000 \bigg( 1 + \dfrac{1}{2 \times 10} \bigg)^{2}$

$\sf \dashrightarrow 5000 \bigg( \dfrac{100 + 1}{2} \bigg)^{2}$

$\sf \dashrightarrow 5000 \bigg( \dfrac{101}{2} \bigg)^{2}$

$\sf \dashrightarrow 5000 \bigg( \dfrac{101^2}{2^2} \bigg)$

$\sf \dashrightarrow 5000 \bigg( \dfrac{10201}{4} \bigg)$

$\sf \dashrightarrow \dfrac{5000 \times 10201}{4}$

$\sf \dashrightarrow \cancel \dfrac{51005000}{4} = 12751250$

Now, we can find the compound interest.

Compound interest :

$\sf \dashrightarrow Amount - Principle$

$\sf \dashrightarrow 12751250 - 5000$

$\dashrightarrow$₹$\sf 12746250$

Hence, the amount. and compound interest are 12751250 and 12746250 rupees respectively.