Question

Find the amount and ci on rupees 20000 at rate 5 percent p a for 1 year intt compounded half yearly

Answer 1

Answer:

Question :-

• Find the amount and compound interest on Rs 20000 at rate of interest 5% p.a for 1 year in compounded half-yearly.

Given :-

• A sum of Rs 20000 at rate of interest 5% p.a for 1 year in compounded half-yearly.

To Find :-

• What is the amount and compound interest.

Formula Used :-

$\clubsuit$ Amount formula when the interest is compounded half-yearly :

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

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 20000
• Rate of Interest = 5% p.a
• Time Period = 1 year

According to the question by using the formula we get,

$\mapsto \bf A =\: P\Bigg(1 + \dfrac{\dfrac{r}{2}}{100}\Bigg)^{2n}$

$\mapsto \sf A =\: 20000\Bigg(1 + \dfrac{\dfrac{5}{2}}{100}\Bigg)^{(2 \times 1)}$

$\mapsto \sf A =\: 20000\bigg(1 + \dfrac{5}{2} \times \dfrac{1}{100}\bigg)^2$

$\mapsto \sf A =\: 20000\bigg(1 + \dfrac{5}{200}\bigg)^2$

$\mapsto \sf A =\: 20000\bigg(\dfrac{200 + 5}{200}\bigg)^2$

$\mapsto \sf A =\: 20000\bigg(\dfrac{205}{200}\bigg)^2$

$\mapsto \sf A =\: 20000\bigg(\dfrac{205}{200} \times \dfrac{205}{200}\bigg)$

$\mapsto \sf A =\: 20000\bigg(\dfrac{42025}{40000}\bigg)$

$\mapsto \sf A =\: 2{\cancel{0000}} \times \dfrac{42025}{4\cancel{0000}}$

$\mapsto \sf A =\: 2 \times \dfrac{42025}{4}$

$\mapsto \sf A =\: \dfrac{2 \times 42025}{4}$

$\mapsto \sf A =\: \dfrac{84050}{4}$

$\mapsto \sf\bold{\purple{A =\: Rs\: 21012.50}}$

✰ Now, we have to find compound interest :

Given :

• Amount = Rs 21012.50
• Principal = Rs 20000

According to the question by using the formula we get,

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

$\dashrightarrow \sf Compound\: Interest =\: Rs\: 21012.50 - Rs\: 20000$

$\dashrightarrow \sf\bold{\red{Compound\: Interest =\: Rs\: 1012.50}}$

$\therefore$ The amount is Rs 21012.50 and compound interest is Rs 1012.50 .