Multiple choice

Gopal invested a certain sum of money that becomes Rs. 11,110 after 4 years and Rs. 16,665 after 8 years on compound interest. Find the sum invested by Gopal.

  1. Rs. 4,440.56

  2. Rs. 7,406.67

  3. Rs. 7,556.67

  4. Rs. 11,110.67

  5. Rs. 5,200.56
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In compound interest, the amount grows in geometric progression. If A1 = P(1+r)^4 = 11110 and A2 = P(1+r)^8 = 16665, then (1+r)^4 = 16665 / 11110 = 1.5. Thus, P = 11110 / 1.5 = 7406.67.

AI explanation

Using the compound interest formula, the amount after 8 years is the amount after 4 years multiplied by the interest multiplier once more. This gives the multiplier as 16665 divided by 11110, which equals 1.5. The initial principal is then found by dividing the 4-year amount by the multiplier squared, yielding 11110 divided by 1.5 squared, which calculates to approximately Rs. 7406.67.

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