Mathematics for FinancePYQ Jan. 21Question 1445 of 512
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Find the future value of annuity of ₹1,000\displaystyle ₹ 1,000 made annually for 7\displaystyle 7 year at interest rate of 14%\displaystyle 14\% compounded annually

Options

A₹10,730.7\displaystyle ₹ 10,730.7
B5,365.35\displaystyle 5,365.35
C8,756\displaystyle 8,756
D9892.34\displaystyle 9892.34
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Correct Answer

✅ Option a — ₹10,730.7\displaystyle ₹ 10,730.7

All Options:

  • A₹10,730.7\displaystyle ₹ 10,730.7
  • B5,365.35\displaystyle 5,365.35
  • C8,756\displaystyle 8,756
  • D9892.34\displaystyle 9892.34

Detailed Solution & Explanation

Let the annual payment of the annuity be A=Rs. 1,000\displaystyle A = \text{Rs. }1,000. Given parameters: * Time (n\displaystyle n) = 7\displaystyle 7 years * Interest Rate (r\displaystyle r) = 14%\displaystyle 14\% p.a., so i=0.14\displaystyle i = 0.14 * Given factor: (1.14)7=2.5023\displaystyle (1.14)^7 = 2.5023 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=1,000×(1.14)7−10.14FV = 1,000 \times \frac{(1.14)^7 - 1}{0.14} FV=1,000×2.5023−10.14FV = 1,000 \times \frac{2.5023 - 1}{0.14} FV=1,000×1.50230.14FV = 1,000 \times \frac{1.5023}{0.14} FV≈1,000×10.7307=10,730.7FV \approx 1,000 \times 10.7307 = 10,730.7 Thus, the future value of the annuity is Rs. 10,730.7\displaystyle \text{Rs. }10,730.7. (Note: While some keys mark Option B, Option A is the mathematically correct value). Hence, **Option A** is the correct answer.

Key Concepts to Understand

Annuity

A sequence of equal periodic payments made at equal intervals of time.

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