Mathematics for FinancePYQ Jan. 21Question 1444 of 512
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₹2,500\displaystyle ₹ 2,500 is paid every year for 10\displaystyle 10 years to pay off a loan. What is the loan amount if interest rate be 14%\displaystyle 14\% p.a. compounded annually?

Options

A₹15,847.90\displaystyle ₹ 15,847.90
B₹13,040.27\displaystyle ₹ 13,040.27
C₹14,674.21\displaystyle ₹ 14,674.21
D₹16,345.11\displaystyle ₹ 16,345.11
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Correct Answer

✅ Option b — ₹13,040.27\displaystyle ₹ 13,040.27

All Options:

  • A₹15,847.90\displaystyle ₹ 15,847.90
  • B₹13,040.27\displaystyle ₹ 13,040.27
  • C₹14,674.21\displaystyle ₹ 14,674.21
  • D₹16,345.11\displaystyle ₹ 16,345.11

Detailed Solution & Explanation

Let the annual payment be A=Rs. 2,500\displaystyle A = \text{Rs. }2,500. Given parameters: * Time (n\displaystyle n) = 10\displaystyle 10 years * Interest Rate (r\displaystyle r) = 14%\displaystyle 14\% p.a., so i=0.14\displaystyle i = 0.14 * Annuity Present Value Factor (P(10,0.14)\displaystyle P(10, 0.14)) ≈5.2161\displaystyle \approx 5.2161 The formula for the Present Value of an ordinary annuity is: PV=A×P(n,i)PV = A \times P(n, i) PV=2,500×5.2161=13,040.25PV = 2,500 \times 5.2161 = 13,040.25 Thus, the loan amount (present value) is approximately Rs. 13,040.27\displaystyle \text{Rs. }13,040.27. Hence, **Option B** is the correct answer.

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