Multiple choice

A sum of Rs. 5,000 amounts to Rs. 7,200 in 8 years at a certain rate per cent p.a, interest compounded yearly. What will be the compound interest on a sum of Rs. 6,550 in 4 years at the same rate of interest?

  1. Rs. 1,290

  2. Rs. 1,285

  3. Rs. 1,415

  4. Rs. 1,310
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

5000(1+r)^8 = 7200 => (1+r)^8 = 1.44 => (1+r)^4 = sqrt(1.44) = 1.2. Compound interest on 6550 in 4 years = 6550 * ((1+r)^4 - 1) = 6550 * (1.2 - 1) = 6550 * 0.2 = 1310.

AI explanation

Let the rate of interest be R. 5000(1 + R/100)^8 = 7200, so (1 + R/100)^8 = 1.44. For the second sum, we need to calculate 6550(1 + R/100)^4. Note that (1 + R/100)^4 is the square root of 1.44, which is 1.2. The final amount is 6550 * 1.2 = 7860. The compound interest is 7860 - 6550 = 1310.

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