Mathematics for FinancePYQ Dec 22Question 1461 of 512
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Mr. A invested 10,000\displaystyle 10,000 every year for next 3\displaystyle 3 years at the interest rate of 8\displaystyle 8 percent per annum compounded annually. What is future value of the annuity?

Options

A32,644\displaystyle 32,644
B32,464\displaystyle 32,464
C32,640\displaystyle 32,640
D32,460\displaystyle 32,460
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Correct Answer

✅ Option b — 32,464\displaystyle 32,464

All Options:

  • A32,644\displaystyle 32,644
  • B32,464\displaystyle 32,464
  • C32,640\displaystyle 32,640
  • D32,460\displaystyle 32,460

Detailed Solution & Explanation

Let the annual investment be A=Rs. 10,000\displaystyle A = \text{Rs. }10,000. Given parameters: * Time (n\displaystyle n) = 3\displaystyle 3 years * Interest Rate (r\displaystyle r) = 8%\displaystyle 8\% p.a. compounded annually, so i=0.08\displaystyle i = 0.08 Assuming it is an ordinary annuity (payments made at the end of each year): FV=A×(1+i)n−1iFV = A \times \frac{(1+i)^n - 1}{i} Substituting the values: FV=10,000×(1.08)3−10.08FV = 10,000 \times \frac{(1.08)^3 - 1}{0.08} FV=10,000×1.259712−10.08FV = 10,000 \times \frac{1.259712 - 1}{0.08} FV=10,000×3.2464=32,464FV = 10,000 \times 3.2464 = 32,464 Thus, the future value of the annuity is Rs. 32,464\displaystyle \text{Rs. }32,464. Hence, **Option B** 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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