Mathematics for FinancePYQ Dec. 21Question 1452 of 512
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The present value of an annuity of ₹25,000\displaystyle ₹ 25,000 to be received after 10\displaystyle 10 years at 6%\displaystyle 6\% per annum compounded annually is

Options

A15,960\displaystyle 15,960
B13,960\displaystyle 13,960
C11,960\displaystyle 11,960
D17,960\displaystyle 17,960
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Correct Answer

✅ Option b — 13,960\displaystyle 13,960

All Options:

  • A15,960\displaystyle 15,960
  • B13,960\displaystyle 13,960
  • C11,960\displaystyle 11,960
  • D17,960\displaystyle 17,960

Detailed Solution & Explanation

Let the present value be PV\displaystyle PV. Given parameters: * Future Value (FV\displaystyle FV) = Rs. 25,000\displaystyle \text{Rs. }25,000 * Time (n\displaystyle n) = 10\displaystyle 10 years * Interest Rate (r\displaystyle r) = 6%\displaystyle 6\% p.a., so i=0.06\displaystyle i = 0.06 The formula for the Present Value of a single sum is: PV=FV(1+i)nPV = \frac{FV}{(1+i)^n} Substituting the values: PV=25,000(1.06)10PV = \frac{25,000}{(1.06)^{10}} First, let's calculate (1.06)10\displaystyle (1.06)^{10}: (1.06)10≈1.790848(1.06)^{10} \approx 1.790848 Now substitute this back: PV=25,0001.790848≈13,959.87PV = \frac{25,000}{1.790848} \approx 13,959.87 Thus, the present value is approximately Rs. 13,960\displaystyle \text{Rs. }13,960. (Note: While some keys mark Option D, the exact mathematical value is Option B). Hence, **Option B** is the correct answer.

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