Multiple choice

Find the sum, if in 4 years it becomes Rs. 600 and in 8 years it becomes Rs. 900 when the rate of interest is compounded annually.

  1. Rs. 400

  2. Rs. 420

  3. Rs. 420.50

  4. Rs. 450

  5. Rs. 440
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A Correct answer
Explanation

For compound interest, A = P(1+r)^t. 600 = P(1+r)^4 and 900 = P(1+r)^8. Dividing the equations: 900/600 = (1+r)^4, so (1+r)^4 = 1.5. Substitute back: 600 = P * 1.5, so P = 600 / 1.5 = 400.

AI explanation

Since the sum grows from Rs. 600 to Rs. 900 over the next four years, the interest earned from year 4 to year 8 is Rs. 300. Applying the compound interest principle to the Rs. 600 balance at year 4, Rs. 600 multiplied by the interest rate for four years equals Rs. 300, meaning the money grows by a factor of 1.5. Because 1.5 is the growth over four years, dividing 600 by 1.5 gives the principal at year zero of Rs. 400, making the result Rs. 400.

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