# A sum of Rs. 400 at compound interest amounts to Rs. 441 in 2 yr. What will be its amount, if the rate of interest is increased by 5%?

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A sum of Rs. 400 at compound interest amounts to Rs. 441 in 2 yr. What will be its amount, if the rate of interest is increased by 5%?
1. Rs. 484
2. Rs. 530
3. Rs. 512
4. Rs. 560

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Correct Answer - Option 1 : Rs. 484

Given:

Sum = Rs.400

Amount = Rs.441

Time = 2 years

Formula Used:

For compound interest,

A = P(1 + R/100)n

where,

A = Amount

P = Sum

R = Rate of interest

n = Number of years

Calculation:

A = P(1 + R/100)n

⇒ 441 = 400(1 + R/100)2

⇒ 441/400 = (1 + R/100)2

⇒ √(441/400) = 1 + R/100

⇒ 21/20 = (100 + R)/100

⇒ 21 = (100 + R)/5

⇒ 105 = 100 + R

⇒ R = 105 – 100

⇒ R = 5%

Now the rate of interest increased by 5%

⇒ Total rate of interest = 5% + 5%

⇒ Total rate of interest = 10%

A = P(1 + R/100)n

⇒ A = 400 (1 + 10/100)2

⇒ A = 400 (1 + 1/10)2

⇒ A = 400 (11/10)2

⇒ A = 400 × 11/10 × 11/10

⇒ A = 4 × 11 × 11

⇒ A = 484

∴ Amount received is Rs.484

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