Mathematics for FinancePYQ May 18Question 1434 of 512
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How much amount is required to be invested every year so as to accumulate 3,00,000\displaystyle 3,00,000 at the end of the 10\displaystyle 10 years, if interest is compounded annually at 10%\displaystyle 10\%?

Options

A18,828.65\displaystyle 18,828.65
B18,328\displaystyle 18,328
C18,828.65\displaystyle 18,828.65
D18,882.65\displaystyle 18,882.65
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Correct Answer

✅ Option a — 18,828.65\displaystyle 18,828.65

All Options:

  • A18,828.65\displaystyle 18,828.65
  • B18,328\displaystyle 18,328
  • C18,828.65\displaystyle 18,828.65
  • D18,882.65\displaystyle 18,882.65

Detailed Solution & Explanation

Let the amount to be invested every year be A\displaystyle A. This is a problem of finding the periodic payment of an ordinary annuity. Given parameters: * Future Value (FV\displaystyle FV) = Rs. 3,00,000\displaystyle \text{Rs. }3,00,000 * Rate of interest (r\displaystyle r) = 10%\displaystyle 10\% p.a., so i=0.10\displaystyle i = 0.10 * Time (n\displaystyle n) = 10\displaystyle 10 years The formula for the Future Value of an ordinary annuity is: FV=A×(1+i)n−1iFV = A \times \frac{(1+i)^n - 1}{i} Substituting the values: 3,00,000=A×(1.10)10−10.103,00,000 = A \times \frac{(1.10)^{10} - 1}{0.10} 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: 3,00,000=A×2.593742−10.103,00,000 = A \times \frac{2.593742 - 1}{0.10} 3,00,000=A×15.937423,00,000 = A \times 15.93742 Solving for A\displaystyle A: A=3,00,00015.93742≈18,823.62A = \frac{3,00,000}{15.93742} \approx 18,823.62 Comparing with the options, the closest value is Rs. 18,828.65\displaystyle \text{Rs. }18,828.65, which is option A (due to rounding conventions of interest factors). Hence, **Option A** is the correct answer.

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