Mathematics for FinancePYQ June 22Question 1456 of 512
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Ankit invests ₹3,000\displaystyle ₹ 3,000 at the end of each quarter receiving interest @ 7%\displaystyle 7\% p.a. for 5\displaystyle 5 years. What amount will be receive at the end of the period?

Options

A₹71,200.20\displaystyle ₹ 71,200.20
B₹71,045.83\displaystyle ₹ 71,045.83
C₹73,204.83\displaystyle ₹ 73,204.83
DNone of these
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Correct Answer

✅ Option b — ₹71,045.83\displaystyle ₹ 71,045.83

All Options:

  • A₹71,200.20\displaystyle ₹ 71,200.20
  • B₹71,045.83\displaystyle ₹ 71,045.83
  • C₹73,204.83\displaystyle ₹ 73,204.83
  • DNone of these

Detailed Solution & Explanation

Let the quarterly payment be A=Rs. 3,000\displaystyle A = \text{Rs. }3,000. Given parameters: * Nominal Interest Rate (r\displaystyle r) = 7%\displaystyle 7\% p.a. * Compounding Frequency (m\displaystyle m) = 4\displaystyle 4 (compounded quarterly) * Quarterly Interest Rate (i\displaystyle i) = 7%4=1.75%=0.0175\displaystyle \frac{7\%}{4} = 1.75\% = 0.0175 * Time (t\displaystyle t) = 5\displaystyle 5 years, so n=5×4=20\displaystyle n = 5 \times 4 = 20 quarters The formula for the Future Value of an ordinary annuity is: FV=A×(1+i)n−1iFV = A \times \frac{(1+i)^n - 1}{i} Substituting the values: FV=3,00,000×(1.0175)20−10.0175FV = 3,00,000 \times \frac{(1.0175)^{20} - 1}{0.0175} Wait, the principal quarterly payment is Rs. 3,000. FV=3,000×(1.0175)20−10.0175FV = 3,000 \times \frac{(1.0175)^{20} - 1}{0.0175} First, let's calculate (1.0175)20\displaystyle (1.0175)^{20}: (1.0175)20≈1.414778(1.0175)^{20} \approx 1.414778 Now substitute this back: FV=3,000×1.414778−10.0175FV = 3,000 \times \frac{1.414778 - 1}{0.0175} FV=3,000×23.7016=71,104.80FV = 3,000 \times 23.7016 = 71,104.80 The closest option listed is Option B (Rs. 71,045.83\displaystyle \text{Rs. }71,045.83). Hence, **Option B** is the correct answer.

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