Question

The C.I compounded yearly during the second year on Rs 100000 at 10% per annum for a period of 2 years is .

Answer 1

Answer:

Given :-

• The sum of Rs 100000 at 10% per annum for a period of 2 years.

To Find :-

• What is the compound interest.

Formula Used :-

$\clubsuit$ Amount formula when the interest is compounded annually :

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

where,

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

$\clubsuit$ Compound Interest or C.I. Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{Compound\: Interest =\: A - P}}}\: \: \: \bigstar$

where,

• A = Amount
• P = Principal

Solution :-

❒ First, we have to find the amount :

Given :

• Principal = Rs 100000
• Rate of Interest = 10% per annum
• Time Period = 2 years

According to the question by using the formula we get,

$\implies \bf A =\: P\bigg(1 + \dfrac{r}{100}\bigg)^n$

$\implies \sf A =\: 100000\bigg(1 + \dfrac{10}{100}\bigg)^2$

$\implies \sf A =\: 100000\bigg(\dfrac{110}{100}\bigg)^2$

$\implies \sf A =\: 100000\bigg(\dfrac{110}{100} \times \dfrac{110}{100}\bigg)$

$\implies \sf A =\: 10{\cancel{0000}} \times \dfrac{12100}{1\cancel{0000}}$

$\implies \sf A =\: 10 \times \dfrac{12100}{1}$

$\implies \sf A =\: 10 \times 12100$

$\implies \sf\bold{\blue{A =\: Rs\: 121000}}$

Hence, the amount is Rs 121000 .

Now, we have to find the compound interest :

Given :

• Amount = Rs 121000
• Principal = Rs 100000

According to the question by using the formula we get,

$\dashrightarrow \bf Compound\: Interest =\: A - P$

$\dashrightarrow \sf Compound\: Interest =\: Rs\: 121000 - Rs\: 100000$

$\dashrightarrow \sf\bold{\red{Compound\: Interest =\: Rs\: 21000}}$

$\sf\bold{\purple{\underline{\therefore\: The\: compound\: interest\: or\: C.I.\: is\: Rs\: 21000\: .}}}$

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