Mathematics for FinanceMTP Apr 21Question 1329 of 512
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A sum amount to Rs. 1331\displaystyle 1331 at a principal of Rs.1000\displaystyle 1000 at 10%\displaystyle 10\% CI. Find the time

Options

A3.31\displaystyle 3.31 years
B4\displaystyle 4 years
C3\displaystyle 3 years
D2\displaystyle 2 years
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Correct Answer

✅ Option c — 3\displaystyle 3 years

All Options:

  • A3.31\displaystyle 3.31 years
  • B4\displaystyle 4 years
  • C3\displaystyle 3 years
  • D2\displaystyle 2 years

Detailed Solution & Explanation

**Derivation of Time Period** Given: - Principal (P\displaystyle P) = Rs. 1,000\displaystyle \text{Rs. }1,000 - Amount (A\displaystyle A) = Rs. 1,331\displaystyle \text{Rs. }1,331 - Rate of Interest (r\displaystyle r) = 10%\displaystyle 10\% per annum compounded annually **Step 1: Set up the Compound Interest equation** A=P(1+r)tA = P(1 + r)^t 1331=1000(1+0.10)t1331 = 1000(1 + 0.10)^t 1.331=(1.10)t1.331 = (1.10)^t **Step 2: Solve for t\displaystyle t** Since (1.10)3=1.331\displaystyle (1.10)^3 = 1.331, we have: (1.10)3=(1.10)t  ⟹  t=3 years(1.10)^3 = (1.10)^t \implies t = 3 \text{ years} Hence, **Option C** is the correct answer.

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