A sum of Rs. 400 at compound interest amounts to Rs. 441 in 2 yr. What

1.	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. 4842. Rs. 5303. Rs. 5124. Rs. 560
Answer» 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

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. 4842. Rs. 5303. Rs. 5124. Rs. 560

Answer» 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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