Question

2. Calculate the amount on 1,60,000 at 10% per annum for 2 years, compounded half yearly.​

Answer 1

Answer:

Given :-

• A sum of Rs 160000 at 10% per annum for 2 years.

To Find :-

• What is the compounded half-yearly.

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

Solution :-

Given :

• Principal = Rs 160000
• Rate of Interest = 10% per annum
• Time Period = 2 years

According to the question by using the formula we get,

$\implies \sf A =\: 160000\bigg(1 + \dfrac{\dfrac{10}{2}}{100}\bigg)^{(2 \times 2)}$

$\implies \sf A =\: 160000\bigg(1 + \dfrac{10}{2} \times \dfrac{1}{100}\bigg)^4$

$\implies \sf A =\: 160000\bigg(1 + \dfrac{1\cancel{0}}{20\cancel{0}}\bigg)^4$

$\implies \sf A =\: 160000\bigg(1 + \dfrac{1}{20}\bigg)^4$

$\implies \sf A =\: 160000\bigg(\dfrac{20 + 1}{20}\bigg)^4$

$\implies \sf A =\: 160000\bigg(\dfrac{21}{20}\bigg)^4$

$\implies \sf A =\: 160000\bigg(\dfrac{21}{20} \times \dfrac{21}{20} \times \dfrac{21}{20} \times \dfrac{21}{20}\bigg)$

$\implies \sf A =\: 160000\bigg(\dfrac{194481}{160000}\bigg)$

$\implies \sf A =\: {\cancel{160000}} \times \dfrac{194481}{\cancel{160000}}$

$\implies \sf\bold{\red{A =\: Rs\: 194481}}$

$\therefore$ The amount is Rs 194481 .

Answer 2

Answer :

• The Amount is Rs.194481

Given :

• A sum of Rs. 1,60,000 at 10% per annum for 2 years

To find :

• Amount

Solution :

Given

• Principal (p) = 160000
• Rate (r) = 10% per annum
• Time (t) = 2 years

We know that

• Amount = p(1 + r/2 / 2/100)2n

Where,

• p is principal
• r is rate

⇢ Amount = p(1 + r/2 / 2/100)2n

⇢ A = 160000(1 + 10/2 / 2/100) 2 × 2

⇢ A = 160000(1 + 10/2 × 1/100) ⁴

⇢ A = 160000(1 + 10/200)⁴

⇢ A = 160000(1 + 1/20)⁴

⇢ A = 160000(20 + 1 / 20)⁴

⇢ A = 160000(21/20)⁴

⇢ A = 160000(21/20 + 21/20 + 21/20 + 21/20)

⇢ A = 160000(194481/160000)

⇢ A = 194481

Hence,

The Amount is Rs.194481