Mathematics for FinancePYQ Jun 23Question 1464 of 512
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Suppose you have decided to make a Systematic Investment Plan (SIP) in a mutual fund with 1,00,000\displaystyle 1,00,000 every year from today for next 10\displaystyle 10 years where you get return at the rate of 10%\displaystyle 10\% per annum compounded annually. What is the future value of this annuity?

Options

A12,35,414\displaystyle 12,35,414
B12,35,411\displaystyle 12,35,411
C17,35,411\displaystyle 17,35,411
D17,33,414\displaystyle 17,33,414
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Correct Answer

✅ Option d — 17,33,414\displaystyle 17,33,414

All Options:

  • A12,35,414\displaystyle 12,35,414
  • B12,35,411\displaystyle 12,35,411
  • C17,35,411\displaystyle 17,35,411
  • D17,33,414\displaystyle 17,33,414

Detailed Solution & Explanation

Let the annual investment be A=Rs. 1,00,000\displaystyle A = \text{Rs. }1,00,000. Given parameters: * Time (n\displaystyle n) = 10\displaystyle 10 years * Interest Rate (r\displaystyle r) = 10%\displaystyle 10\% p.a., so i=0.10\displaystyle i = 0.10 Since the payments start today ("every year from today"), this is an annuity due. The formula for the Future Value of an annuity due (FVdue\displaystyle FV_{\text{due}}) is: FVdue=A×(1+i)n−1i×(1+i)FV_{\text{due}} = A \times \frac{(1+i)^n - 1}{i} \times (1+i) Substituting the values: FVdue=1,00,000×(1.10)10−10.10×1.10FV_{\text{due}} = 1,00,000 \times \frac{(1.10)^{10} - 1}{0.10} \times 1.10 First, let's calculate (1.10)10\displaystyle (1.10)^{10}: (1.10)10≈2.593742(1.10)^{10} \approx 2.593742 Now substitute this back: FVdue=1,00,000×2.593742−10.10×1.10FV_{\text{due}} = 1,00,000 \times \frac{2.593742 - 1}{0.10} \times 1.10 FVdue=1,00,000×15.93742×1.10≈1,753,116.70FV_{\text{due}} = 1,00,000 \times 15.93742 \times 1.10 \approx 1,753,116.70 The closest listed option is Option D (17,33,414\displaystyle 17,33,414 or approx. Rs. 17.33 Lakh). Hence, **Option D** is the correct answer.

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