Question

the simple interest on a sum of money for 2 years at5%per annum is rs 40 what will be compound interest for the same​

Answer 1

Given

• Time = 2 years
• Rate % = 5%
• Simple Interest = Rs. 40

To find

• Compound Interest

Solution

• Formula to be used :-

$\sf{s.i. = \cfrac{p \times r \times t}{100}}$

where,

• S.I. = Simple Interest
• P = Principal
• R = Rate%
• T = Time

Substituting the given values,

$: \implies \sf 40 = \cfrac{p \times 5 \times 2}{100}$

$: \implies \sf 40 = \cfrac{p \times 10}{100}$

$: \implies \sf 40 = \cfrac{p \times 1 \not0}{10 \not0}$

$: \implies \sf 40 = \cfrac{p}{10}$

$: \implies \sf 40 \times 10 = p$

$: \implies \sf 400 = p$

$\bigstar \: \: \bf \pink{principal = rs.400}$

• Formula to be used :-

• Amount = P(1 + r/100)ⁿ

Substituting the given values,

⟶ 400(1 + 5/100)²

⟶ 400(1 + 1/20)²

⟶ 400(21/20)²

⟶ 400 × 21/20 × 21/20

$\bf \pink{amount = Rs.441}$

• Formula to be used :-

• Compound Interest = Amount - Principal

Substituting the values,

⟶ Rs. 441 - Rs. 400

⟶ Rs. 41

$\bigstar \: \: \bf \underline \red{compound \: \: \: interest = \: Rs.41}$

Answer 2

Let the sum=P Rs.

S.I=50 Rs.

Rate of interest=5 %

Time =2 years.

S.I=P×R×T/100

50=P×5×5/100

P=50x100/5x2=500Rs.

C.I. of 500 Rs

Amount=500(1+5/100)^2

⇒500×105/100 x 105/100

⇒500×21/20 x 21/20

⇒551.25

C.I=551−500−51.25Rs.

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