# A sum amounts to Rs. 7,562 in 4 years and to Rs. 8,469.44 in 5 years. at a certain rate percent per annum when the interest is compounded yearly. If R

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A sum amounts to Rs. 7,562 in 4 years and to Rs. 8,469.44 in 5 years. at a certain rate percent per annum when the interest is compounded yearly. If Rs. 10,000 at the same rate of interest is borrowed for two years, then what will be the compound interest (in Rs.) ?
1. 1,965
2. 1,736
3. 2,764
4. 2,544

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Correct Answer - Option 4 : 2,544

Given:

Amount after 4 years (A4) = Rs. 7,562

Amount after 5 years (A5) = Rs. 8,469.44

Principal (P) = Rs. 10,000

Formula used:

CI = P × [(1 + R/100)n – 1]

Where CI is compound interest, P is principal, R is rate percent, and n is time in years

Calculation:

Let the rate of interest be R%

CI for fifth year = A5 – A4 = 8,469.44 – 7562

⇒ CI for fifth year = 907.44

CI for fifth year = R% of A4

⇒ 907.44 = (R/100) × 7562

⇒ R = 90744/7562

⇒ R = 12%

CI = 10,000 × [(1 + 12/100)2 – 1]

⇒ CI = 10000 × 0.2544

∴ CI is Rs. 2,544