Mathematics for FinancePYQ Jun 23Question 1249 of 512
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Jonny wants to have 2,00,000\displaystyle 2,00,000 in his saving account after three years. The rate of interest offered by bank is 8%\displaystyle 8\% per annum compounded annually. How much should he invest today to achieve his target amount?

Options

A1,47,489.10\displaystyle 1,47,489.10
B1,58,766.44\displaystyle 1,58,766.44
C1,71,035.59\displaystyle 1,71,035.59
D1,84,417.96\displaystyle 1,84,417.96
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Correct Answer

✅ Option b — 1,58,766.44\displaystyle 1,58,766.44

All Options:

  • A1,47,489.10\displaystyle 1,47,489.10
  • B1,58,766.44\displaystyle 1,58,766.44
  • C1,71,035.59\displaystyle 1,71,035.59
  • D1,84,417.96\displaystyle 1,84,417.96

Detailed Solution & Explanation

**Derivation of Invested Principal** Given: - Future Value (A\displaystyle A) = Rs. 2,00,000\displaystyle \text{Rs. }2,00,000 - Time (t\displaystyle t) = 3\displaystyle 3 years - Rate of Interest (r\displaystyle r) = 8%\displaystyle 8\% per annum compounded annually **Step 1: Calculate the Present Value (P\displaystyle P)** A=P(1+r)tA = P(1 + r)^t 200000=P(1+0.08)3200000 = P(1 + 0.08)^3 200000=P(1.08)3200000 = P(1.08)^3 200000=P(1.259712)200000 = P(1.259712) P=2000001.259712≈Rs. 1,58,766.44P = \frac{200000}{1.259712} \approx \text{Rs. }1,58,766.44 Hence, **Option B** is the correct answer.

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