Mathematics for FinancePYQ Dec 21Question 1230 of 512
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R needs money to pay 5,00,000\displaystyle 5,00,000 in 10\displaystyle 10 years. He invested a sum in a scheme at 9%\displaystyle 9\% rate of interest compounded half-yearly. How much amount (in )heinvested?\displaystyle ) he invested?1.046^{20}=2.41171$

Options

A3,07,321\displaystyle 3,07,321
B2,70,321\displaystyle 2,70,321
C2,07,321\displaystyle 2,07,321
D3,40,321\displaystyle 3,40,321
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Correct Answer

✅ Option c — 2,07,321\displaystyle 2,07,321

All Options:

  • A3,07,321\displaystyle 3,07,321
  • B2,70,321\displaystyle 2,70,321
  • C2,07,321\displaystyle 2,07,321
  • D3,40,321\displaystyle 3,40,321

Detailed Solution & Explanation

**Derivation of Invested Principal** Given: - Target Future Value (A\displaystyle A) = Rs. 5,00,000\displaystyle \text{Rs. }5,00,000 - Time (t\displaystyle t) = 10\displaystyle 10 years - Rate of Interest (r\displaystyle r) = 9%\displaystyle 9\% per annum compounded half-yearly - Given: (1.045)20≈2.41171\displaystyle (1.045)^{20} \approx 2.41171 (adjusted from typo 1.04620\displaystyle 1.046^{20} in question text) **Step 1: Calculate periodic rate (i\displaystyle i) and number of periods (n\displaystyle n)** - Periodic rate i=r2=9%2=4.5%=0.045\displaystyle i = \frac{r}{2} = \frac{9\%}{2} = 4.5\% = 0.045 - Number of periods n=t×2=10×2=20\displaystyle n = t \times 2 = 10 \times 2 = 20 half-years. **Step 2: Calculate the Principal (P\displaystyle P)** A=P(1+i)nA = P(1 + i)^n 500000=P(1+0.045)20500000 = P(1 + 0.045)^{20} 500000=P(1.045)20500000 = P(1.045)^{20} Using the given value (1.045)20=2.41171\displaystyle (1.045)^{20} = 2.41171: 500000=P×2.41171500000 = P \times 2.41171 P=5000002.41171≈Rs. 2,07,321.77≈Rs. 2,07,321P = \frac{500000}{2.41171} \approx \text{Rs. }2,07,321.77 \approx \text{Rs. }2,07,321 Hence, **Option C** 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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