Question

find the principal which will amount to 8820 rs in 2 yrs at 5% per annum compoud interest .​

Answer 1

Answer:

Given :-

• A sum of amount of Rs 8820 in 2 years at the rate of 5% per annum compound interest.

To Find :-

• What is the principal of the amount.

Formula Used :-

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

where,

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

Solution :-

Let, the principal be x

Given :

• Amount = Rs 8820
• Rate of Interest = 5%
• Time = 2 years

According to the question by using the formula we get,

⇒ $\sf 8820\: =\: x\bigg(1 + \dfrac{5}{100}\bigg)^{2}$

⇒ $\sf 8820\: =\: x\bigg(\dfrac{105}{100}\bigg)^{2}$

⇒ $\sf 8820\: =\: x \times \dfrac{105}{100} \times \dfrac{105}{100}$

⇒ $\sf 8820\: =\: \dfrac{11025x}{100 \times 100}$

By doing cross multiplication we get,

⇒ $\sf 11025x\: =\: 8820 \times 100 \times 100$

⇒ $\sf x\: =\: \dfrac{8820 \times 100 \times 100}{11025}$

⇒ $\sf x\: =\: \dfrac{88200000}{11025}$

⇒ $\sf x\: =\: \dfrac{\cancel{88200000}}{\cancel{11025}}$

➠ $\sf\red{x\: =\: Rs\: 8000}$

Hence, we take principal as x, so the principal is Rs 8000

$\therefore$ The principal of a sum is Rs 8000 .

Answer 2

$\huge\sf{Answer :- }$

Given :-

• Amount = ₹8820

• Rate of interest(r) = 5%

• Time(n) = 2 years

To Find :-

• Principal

Solution :-

Let the Principal be p

We know that,

$\large\sf{Amount = p(1 + \frac{r}{100}) {n}^{} }$

By substituting values,

$\large\sf{➙ ₹8820 = p(1 + \frac{5}{100} ) ^{2} }$

$\large\sf{➙ ₹8820 = p( \frac{100 + 5}{100}) ^{2} }$

$\large\sf{➙ ₹8820 = p(\frac{105}{100} ) ^{2} }$

$\large\sf{➙ ₹8820 = p( \frac{105}{100} \times \frac{105}{100} ) }$

$\large\sf{➙ ₹8820 = p( \frac{11025}{100 \times 100} )}$

$\large\sf{➙ ₹8820 = \frac{11025p}{100 \times 100} }$

By using Butterfly method,

$\large\sf{ ➙ 11025p = 100 \times 100 \times 8820}$

$\large\sf{➙ 11025p = 88200000}$

$\large\sf{➙ p = \frac{88200000}{11025}}$

➥ p = ₹8000

Hence, The principal is ₹8000