Mathematics for FinancePYQ Dec 23Question 1467 of 512
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Govinda's mother decides to gift him 50,000\displaystyle 50,000 every year starting from today for the next five years. Govinda deposits this amount in a bank as and when he receives and gets 10%\displaystyle 10\% per annum interest rate, compounded annually. What is the present value of this annuity? Given P(4,0.10)=3.16987\displaystyle P(4,0.10) = 3.16987.

Options

A2,80,493.5\displaystyle 2,80,493.5
B2,08,493.5\displaystyle 2,08,493.5
C2,08,943.5\displaystyle 2,08,943.5
D2,58,493.5\displaystyle 2,58,493.5
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Correct Answer

✅ Option a — 2,80,493.5\displaystyle 2,80,493.5

All Options:

  • A2,80,493.5\displaystyle 2,80,493.5
  • B2,08,493.5\displaystyle 2,08,493.5
  • C2,08,943.5\displaystyle 2,08,943.5
  • D2,58,493.5\displaystyle 2,58,493.5

Detailed Solution & Explanation

Let the principal amount be P\displaystyle P. The rate of interest is r=5%\displaystyle r = 5\% p.a., so i=5100=0.05\displaystyle i = \frac{5}{100} = 0.05. The time period is t=2\displaystyle t = 2 years. The formula for the difference between Compound Interest (CI\displaystyle CI) and Simple Interest (SI\displaystyle SI) for a 2\displaystyle 2-year period is: CI−SI=P×i2CI - SI = P \times i^2 Given that the difference is Rs. 21\displaystyle \text{Rs. }21: 21=P×(0.05)221 = P \times (0.05)^2 21=P×0.002521 = P \times 0.0025 Solving for P\displaystyle P: P=210.0025=8,400P = \frac{21}{0.0025} = 8,400 Thus, the principal amount is Rs. 8,400\displaystyle \text{Rs. }8,400. (Note: While some keys mark Option D, the mathematically correct value is Option A). Hence, **Option A** is the correct answer.

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