Question

3. Find the compound interest on Rs 90,000 for 3 years at the rate of 10% per annum compounded annually.​

Answer 1

Answer:

Given :-

• A sum of Rs 90000 for 3 years at the rate of 10% per annum compounded annually.

To Find :-

• What is the compound interest.

Formula Used :-

$\clubsuit$ Amount Formula :

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

where,

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

$\clubsuit$ Compound Interest 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 90000
• Rate of Interest = 10% per annum
• Time Period = 3 years

According to the question by using the formula we get,

$\implies \sf A =\: 90000\bigg(1 + \dfrac{1\cancel{0}}{10\cancel{0}}\bigg)^3$

$\implies \sf A =\: 90000\bigg(1 + \dfrac{1}{10}\bigg)^3$

$\implies \sf A =\: 90000\bigg(\dfrac{10 + 1}{10}\bigg)^3$

$\implies \sf A =\: 90000\bigg(\dfrac{11}{10}\bigg)^3$

$\implies \sf A =\: 90000\bigg(\dfrac{11}{10} \times \dfrac{11}{10} \times \dfrac{11}{10}\bigg)$

$\implies \sf A =\: 90000\bigg(\dfrac{1331}{1000}\bigg)$

$\implies \sf A =\: 90{\cancel{000}} \times \dfrac{1331}{1\cancel{000}}$

$\implies \sf A =\: 90 \times 1331$

$\implies \sf\bold{\purple{A =\: Rs\: 119790}}$

Now, we have to find the compound interest :

Given :

• Amount = Rs 119790
• Principal = Rs 90000

According to the question by using the formula we get,

$\dashrightarrow \sf Compound\: Interest =\: Rs\: 119790 - Rs\: 90000$

$\dashrightarrow \sf\bold{\red{Compound\: Interest =\: Rs\: 29790}}$

$\therefore$ The compound interest is Rs 29790 .