Question

What sum will the C.I for 2 yrs at 4%p.a will be 5712 Rs

Answer 1

Given : -

• Compound Interest ,C.I = ₹5712

• Time,n = 2 years

• Rate,r = 4%

To find out:-

Find the Principal,P.

Formula used:-

• A = P ( 1 + r/100 ) ⁿ

• Compound Interest = Amount - Principal

Solution:-

We know that,

Compound Interest = Amount - Principal

⇒ CI = A - P

⇒ 5712 = A - P

⇒ A = 5712 + P

Now,

A = P ( 1 + r/100 ) ⁿ

★ Substituting the values in the above formula,we get:

⇒ 5712 + P = P ( 1 + 4/100 ) ²

⇒ 5712 + P = P ( 1 + 1/25 ) ²

⇒ 5712 + P = P (25 + 1 / 25 )²

⇒ 5712 + P = P ( 26/25 )²

⇒ 5712 + P = P × 676/625

⇒ 5712 + P = 676P / 625

⇒ ( 5712 + P ) 625 = 676P

⇒ 5712 × 625 + 625P = 676P

⇒ 5712 × 625 = 676P - 625P

⇒ 3,570,000 = 51P

⇒ 51P = 3,570,000

⇒ P = 3,570,000/51

⇒ P = Rs. 70,000

Hence, the sum will be Rs 70,000.

Answer 2

$\bf{\underline{\underline \blue{Solution:-}}}$

$\sf\underline{\red{\:\:\: AnswEr:-\:\:\:}}$

• The sum will be Rs 70,000

$\sf\underline{\red{\:\:\: Given:-\:\:\:}}$

• Compound Interest = Rs 5712
• Time Given = 2 years
• Rate Given = 4% p.a

$\sf\underline{\red{\:\:\: Need\:To\: Find:-\:\:\:}}$

• The sum will be = ?

$\bf{\underline{\underline \blue{Explanation:-}}}$

$\sf\underline{\pink{\:\:\: Formula\:Used\: Here:-\:\:\:}}$

$\bigstar \: \boxed{ \sf \: Compound\: Interest = Amount - Principal }$

$\sf\underline{\red{\:\:\: Now, Putting\:the\: values:-\:\:\:}}$

$\dashrightarrow \sf { 5712 = Amount - Principal}$

$\dashrightarrow \sf { Amount = 5712 + Principal}$

$\sf\underline{\pink{\:\:\:Again,\: Formula\: Used\:Here:-\:\:\:}}$

$\bigstar \: \boxed{ \sf \: Amount = P \bigg(1 + \frac{R}{100}\bigg)^n }$

$\sf\underline{\red{\:\:\:Now, Putting\:the\: values:-\:\:\:}}$

$\dashrightarrow \sf {5712 + P = P\bigg(1+ \frac{4}{100}\bigg)^2}$

$\dashrightarrow \sf {5712 + P = P \bigg(1 + \frac{1}{25}\bigg)^2}$

$\dashrightarrow \sf {5712 + P = P\bigg(\frac{26}{25}\bigg)^2}$

$\dashrightarrow \sf {5712 + P = P\bigg(\frac{676}{625}\bigg) }$

$\dashrightarrow \sf {5712 + P = \frac{676P}{ 625} }$

$\dashrightarrow \sf {625P + 5712 \times 625 = 676P}$

$\dashrightarrow \sf {5712 \times 625 = 676P - 625P}$

$\dashrightarrow \sf {5712 \times 625 = 51P}$

$\dashrightarrow \sf {Principal = \frac{(5712 \times 625)}{51} }$

$\dashrightarrow \sf {Principal = 112 \times 625}$

$\dashrightarrow \sf {Principal = 70,000}$

$\sf\underline{\green{\:\:\: ThereFore:-\:\:\:}}$

• The sum will be Rs 70,000.

$\rule{200}{2}$