Question

*Find the compound interest on Rs. 1000 for 2 years at 10% rate of interest compounded annually?*

1️⃣ Rs. 1200
2️⃣ Rs. 1000
3️⃣ Rs. 1210
4️⃣ Rs. 210​

Answer 1

Answer:

Given :-

• A sum of Rs 1000 for 2 years at 10% rate of Interest compounded annually.

To Find :-

• What is the compound interest.

Formula Used :-

❶ To find amount we know that,

${\red{\boxed{\large{\bold{A =\: P\bigg(1 + \dfrac{r}{100}\bigg)^{n}}}}}}$

where,

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

❷ To find compound interest we know that,

${\red{\boxed{\large{\bold{C.I =\: A -\: P}}}}}$

where,

• C.I = Compound Interest
• A = Amount
• P = Principal

Solution :-

❶ First we have to find the amount,

Given :

• Principal (P) = Rs 1000
• Rate of Interest (r) = 10%
• Time (t) = 2 years

According to the question by using the formula we get,

⇒ $\sf A =\: 1000\bigg(1 + \dfrac{10}{100}\bigg)^{2}$

⇒ $\sf A =\: 1000\bigg(\dfrac{100 + 10}{100}\bigg)^{2}$

⇒ $\sf A =\: 1000\bigg(\dfrac{110}{100}\bigg)^{2}$

⇒ $\sf A =\: 1000 \times \dfrac{110}{\cancel{100}} \times \dfrac{110}{100}$

⇒ $\sf A =\: 1\cancel{000} \times \dfrac{110}{1\cancel{00}} \times \dfrac{110}{10\cancel{0}}$

⇒ $\sf A =\: \dfrac{1210\cancel{0}}{1\cancel{0}}$

➠ $\sf\bold{\green{A =\: Rs\: 1210}}$

Hence, the amount is Rs 1210 .

❷ Now we have to find the compound interest,

Given :

• Amount (A) = Rs 1210
• Principal (P) = Rs 1000

According to the question by using the formula we get,

↦ $\sf C.I =\: Rs\: 1210 -\: Rs\: 1000$

➦ $\sf\bold{\purple{C.I =\: Rs\: 210}}$

$\therefore$ The compound interest is Rs 210 . Hence, the correct options is option no 4) Rs 210.