Question

find the compound interest on 3000 at the rate of 6% for one by 1/1/2 year compound half yearly​

Answer 1

★ Solution :-

First, we should find the amount of the given values. We have an formula to find the same. It's mentioned below,

Amount :-

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

$\sf \leadsto 3000 \bigg(1 + \dfrac{6}{100} \bigg)^{1 \dfrac{1}{2} (2)}$

$\sf \leadsto 3000 \bigg(1 + \dfrac{6}{100} \bigg)^{\dfrac{3}{2} (2)}$

$\sf \leadsto 3000 \bigg(1 + \dfrac{6}{100} \bigg)^{\dfrac{6}{2}}$

$\sf \leadsto 3000 \bigg(1 + \dfrac{6}{100} \bigg)^{3}$

$\sf \leadsto 3000 \bigg(1 + \dfrac{3}{50} \bigg)^{3}$

$\sf \leadsto 3000 \bigg( \dfrac{50 + 3}{50} \bigg)^{3}$

$\sf \leadsto 3000 \bigg( \dfrac{53}{50} \bigg)^{3}$

$\sf \leadsto 3000 \bigg( \dfrac{53^3}{50^3} \bigg)$

$\sf \leadsto 3000 \bigg( \dfrac{148877}{125000} \bigg)$

$\sf \leadsto 3 \bigg( \dfrac{148877}{125} \bigg)$

$\sf \leadsto \dfrac{3 \times 148877}{125} = \dfrac{446631}{125}$

$\sf \leadsto \cancel \dfrac{446631}{125} = 3573.048$

Now, we can find the compound interest.

Compound interest :-

$\sf \leadsto CI = Amount - Principle$

$\sf \leadsto 3573.048 - 3000$

$\sf \leadsto Rs \: . \: 573.048$

Therefore, the compound interest is ₹573.048.

Answer 2

Answer:

Given :-

• A sum of Rs 3000 at the rate of 6% for 1½ year compounded half-yearly.

To Find :-

• What is the compound interest.

Solution :-

First, we have to find the amount :

Given :

• Principal = Rs 3000
• Rate of Interest = 6%
• Time = 1½ year

As we know that :

$\mapsto \sf\boxed{\bold{\pink{A =\: P\bigg\{1 + \dfrac{r}{100}\bigg\}^{(n \times 2)}}}}$

where,

• A = Amount
• P = Principal
• r = Rate of Interest
• n = Time Period

According to the question by using the formula we get,

$\mapsto \sf Amount =\: 3000\bigg\{1 + \dfrac{6}{100}\bigg\}^{(1\frac{1}{2} \times 2)}$

$\mapsto \sf Amount =\: 3000\bigg\{\dfrac{106}{100}\bigg\}^{(\frac{3}{2} \times 2)}$

$\mapsto \sf Amount =\: 3000\bigg\{\dfrac{106}{100}\bigg\}^{(\frac{\cancel{6}}{\cancel{2}})}$

$\mapsto \sf Amount =\: 3000\bigg\{\dfrac{106}{100}\bigg\}^{3}$

$\mapsto \sf Amount =\: 3000 \times \dfrac{106}{100} \times \dfrac{106}{100} \times \dfrac{106}{100}$

$\mapsto \sf Amount =\: \dfrac{\cancel{3573048000}}{\cancel{1000000}}$

$\mapsto \sf\bold{\purple{Amount =\: Rs\: 3573.048}}$

Now, we have to find the compound interest :

As we know that :

$\mapsto \sf\boxed{\bold{\pink{C.I =\: Amount - Principal}}}$

where,

• C.I = Compound Interest

Given :

• Amount = Rs 3573.048
• Principal = Rs 3000

According to the question by using the formula we get,

$\longrightarrow \sf C.I =\: Rs\: 3573.048 - Rs\: 3000$

$\longrightarrow \sf\bold{\red{C.I =\: Rs\: 573.048}}$

$\therefore$ The compound interest is Rs 573.048.