Mathematics for FinancePYQ Dec 23Question 1470 of 512
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What will be the future value of an annuity of 2,500\displaystyle 2,500 made annually for 12\displaystyle 12 years at interest rate of 5%\displaystyle 5\% compounded annually

Options

A37,588.58\displaystyle 37,588.58
B39,790.00\displaystyle 39,790.00
C40,873.13\displaystyle 40,873.13
D42,603.68\displaystyle 42,603.68
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Correct Answer

✅ Option a — 37,588.58\displaystyle 37,588.58

All Options:

  • A37,588.58\displaystyle 37,588.58
  • B39,790.00\displaystyle 39,790.00
  • C40,873.13\displaystyle 40,873.13
  • D42,603.68\displaystyle 42,603.68

Detailed Solution & Explanation

Let the principal sum be P\displaystyle P. Given parameters: * Final Amount (A\displaystyle A) = Rs. 1,20,000\displaystyle \text{Rs. }1,20,000 * Nominal Interest Rate (r\displaystyle r) = 4%\displaystyle 4\% p.a. * Compounding Frequency (m\displaystyle m) = 2\displaystyle 2 (compounded semi-annually) * Semi-annual Interest Rate (i\displaystyle i) = 4%2=2%=0.02\displaystyle \frac{4\%}{2} = 2\% = 0.02 * Time (t\displaystyle t) = 1\displaystyle 1 year, so number of periods n=1×2=2\displaystyle n = 1 \times 2 = 2 semi-annual periods The formula for compound amount is: A=P(1+i)nA = P(1+i)^n Substituting the values: 1,20,000=P(1.02)21,20,000 = P(1.02)^2 1,20,000=P×1.04041,20,000 = P \times 1.0404 Solving for P\displaystyle P: P=1,20,0001.0404≈1,15,340.25P = \frac{1,20,000}{1.0404} \approx 1,15,340.25 Thus, the principal sum is approximately Rs. 1,15,340\displaystyle \text{Rs. }1,15,340. Hence, **Option A** is the correct answer.

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