Mathematics for FinancePYQ Nov 20Question 1207 of 512
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A certain sum invested at 4%\displaystyle 4\% per annum compounded semi-annually amounts to 1,20,000\displaystyle 1,20,000 at the end of one year. Find the sum:

Options

A1,15,340\displaystyle 1,15,340
B1,10,120\displaystyle 1,10,120
C1,12,812\displaystyle 1,12,812
D1,13,113\displaystyle 1,13,113
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Correct Answer

✅ Option a — 1,15,340\displaystyle 1,15,340

All Options:

  • A1,15,340\displaystyle 1,15,340
  • B1,10,120\displaystyle 1,10,120
  • C1,12,812\displaystyle 1,12,812
  • D1,13,113\displaystyle 1,13,113

Detailed Solution & Explanation

**Derivation of Principal Amount** Given: - Amount (A\displaystyle A) = Rs. 1,20,000\displaystyle \text{Rs. }1,20,000 - Rate of Interest (r\displaystyle r) = 4%\displaystyle 4\% per annum compounded semi-annually - Time (t\displaystyle t) = 1\displaystyle 1 year **Step 1: Calculate periodic rate (i\displaystyle i) and number of periods (n\displaystyle n)** - Periodic rate i=r2=4%2=2%=0.02\displaystyle i = \frac{r}{2} = \frac{4\%}{2} = 2\% = 0.02 per half-year. - Number of periods n=t×2=1×2=2\displaystyle n = t \times 2 = 1 \times 2 = 2 half-years. **Step 2: Calculate Principal (P\displaystyle P)** A=P(1+i)nA = P(1 + i)^n 120000=P(1+0.02)2120000 = P(1 + 0.02)^2 120000=P(1.02)2120000 = P(1.02)^2 120000=1.0404P120000 = 1.0404 P P=1200001.0404≈Rs. 1,15,340.25P = \frac{120000}{1.0404} \approx \text{Rs. }1,15,340.25 Hence, **Option A** is the correct answer.

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If Rs. 1,000\displaystyle \text{Rs. }1,000 be invested at interest rate of 5%\displaystyle 5\% and the interest be added to the principal every 10\displaystyle 10 years, then the number in years in which it will amount to Rs. 2,000\displaystyle \text{Rs. }2,000 is:

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