Mathematics for FinancePYQ Sep 24Question 1265 of 512
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Kanta wants to accumulate 4,91,300\displaystyle 4,91,300 in her savings account after three years. The rate of interest offered by bank is 6%\displaystyle 6\% per annum compounded annually. How much amount should she invest today to achieve her target amount?

Options

A4,37,500\displaystyle 4,37,500
B4,09,600\displaystyle 4,09,600
C46,900\displaystyle 46,900
D49,600\displaystyle 49,600
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Correct Answer

✅ Option b — 4,09,600\displaystyle 4,09,600

All Options:

  • A4,37,500\displaystyle 4,37,500
  • B4,09,600\displaystyle 4,09,600
  • C46,900\displaystyle 46,900
  • D49,600\displaystyle 49,600

Detailed Solution & Explanation

**Derivation of Invested Principal** *Note: The question contains a typo in the interest rate, stating it is 6% per annum. The options correspond to a rate of 6.25% per annum (17/16=1.0625\displaystyle 17/16 = 1.0625). We present the mathematically clean solution using 6.25%.* Given: - Target Future Value (A\displaystyle A) = Rs. 4,91,300\displaystyle \text{Rs. }4,91,300 - Rate of Interest (r\displaystyle r) = 6.25%\displaystyle 6.25\% per annum compounded annually - Time (t\displaystyle t) = 3\displaystyle 3 years **Step 1: Set up the Compound Interest equation** A=P(1+r)tA = P(1 + r)^t 491300=P(1+0.0625)3491300 = P(1 + 0.0625)^3 491300=P(1.0625)3491300 = P(1.0625)^3 **Step 2: Express the term in fractions** 1.0625=17161.0625 = \frac{17}{16} 491300=P(1716)3491300 = P \left(\frac{17}{16}\right)^3 491300=P×49134096491300 = P \times \frac{4913}{4096} **Step 3: Solve for P\displaystyle P** P=491300×40964913P = 491300 \times \frac{4096}{4913} P=100×4096=Rs. 4,09,600P = 100 \times 4096 = \text{Rs. }4,09,600 Hence, **Option B** is the correct answer.

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