Mathematics for FinanceMTP Nov 18Question 1486 of 512
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Find the future value of annuity 1000\displaystyle 1000 made annually for 7\displaystyle 7 years at interest rate of 14%\displaystyle 14\% compounded annually is

Options

A10730.71\displaystyle 10730.71
B10735\displaystyle 10735
C10734\displaystyle 10734
D10937\displaystyle 10937
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Correct Answer

✅ Option a — 10730.71\displaystyle 10730.71

All Options:

  • A10730.71\displaystyle 10730.71
  • B10735\displaystyle 10735
  • C10734\displaystyle 10734
  • D10937\displaystyle 10937

Detailed Solution & Explanation

The future value (FV\displaystyle FV) of an ordinary annuity is: FV=A[(1+i)n−1i]FV = A \left[ \frac{(1+i)^n - 1}{i} \right] Given: * Annual payment (A\displaystyle A) = 1,000\displaystyle 1,000 * Time (n\displaystyle n) = 7\displaystyle 7 years * Interest rate (i\displaystyle i) = 14%\displaystyle 14\% p.a. = 0.14\displaystyle 0.14 Substituting the values: FV=1,000[(1.14)7−10.14]FV = 1,000 \left[ \frac{(1.14)^7 - 1}{0.14} \right] Using (1.14)7≈2.502298\displaystyle (1.14)^7 \approx 2.502298: FV=1,000[2.502298−10.14]=1,000×10.7307=10,730.70FV = 1,000 \left[ \frac{2.502298 - 1}{0.14} \right] = 1,000 \times 10.7307 = 10,730.70 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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