Mathematics for FinancePYQ Dec 22Question 1460 of 512
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Raju invests ₹20,000\displaystyle ₹ 20,000 every year in a deposit scheme starting from today for next 12\displaystyle 12 years. Assuming that interest rate on this deposit is 7%\displaystyle 7\% per annum compounded annually. What will be the future value of this annuity?

Options

A₹540,526\displaystyle ₹ 540,526
B382,813\displaystyle 382,813
C643,483\displaystyle 643,483
D357,769\displaystyle 357,769
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Correct Answer

✅ Option b — 382,813\displaystyle 382,813

All Options:

  • A₹540,526\displaystyle ₹ 540,526
  • B382,813\displaystyle 382,813
  • C643,483\displaystyle 643,483
  • D357,769\displaystyle 357,769

Detailed Solution & Explanation

Let the annual investment be A=Rs. 20,000\displaystyle A = \text{Rs. }20,000. Given parameters: * Time (n\displaystyle n) = 12\displaystyle 12 years * Interest Rate (r\displaystyle r) = 7%\displaystyle 7\% p.a., so i=0.07\displaystyle i = 0.07 Since the investment starts 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=20,000×(1.07)12−10.07×1.07FV_{\text{due}} = 20,000 \times \frac{(1.07)^{12} - 1}{0.07} \times 1.07 First, let's calculate (1.07)12\displaystyle (1.07)^{12}: (1.07)12≈2.252192(1.07)^{12} \approx 2.252192 Now substitute this back: FVdue=20,000×2.252192−10.07×1.07FV_{\text{due}} = 20,000 \times \frac{2.252192 - 1}{0.07} \times 1.07 FVdue=20,000×1.2521920.07×1.07FV_{\text{due}} = 20,000 \times \frac{1.252192}{0.07} \times 1.07 FVdue=20,000×17.88846×1.07=3,82,813FV_{\text{due}} = 20,000 \times 17.88846 \times 1.07 = 3,82,813 Thus, the future value of the annuity is approximately Rs. 3,82,813\displaystyle \text{Rs. }3,82,813. Hence, **Option B** is the correct answer.

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