Mathematics for FinanceMTP Dec 23 Series IIQuestion 1529 of 512
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How much amount is required to be invested every year as to accumulate 6,00,000\displaystyle 6,00,000 at the end of 10th\displaystyle 10^{th} year, if interest is compounded annually at 10%\displaystyle 10\% rate of interest?

Options

A37,467\displaystyle 37,467
B37,476\displaystyle 37,476
C37,647\displaystyle 37,647
D37,674\displaystyle 37,674
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Correct Answer

✅ Option b — 37,476\displaystyle 37,476

All Options:

  • A37,467\displaystyle 37,467
  • B37,476\displaystyle 37,476
  • C37,647\displaystyle 37,647
  • D37,674\displaystyle 37,674

Detailed Solution & Explanation

The annual contribution (A\displaystyle A) required to accumulate a future sum FV\displaystyle FV is: A=FV[(1+i)n−1i]A = \frac{FV}{\left[ \frac{(1+i)^n - 1}{i} \right]} Given: * Future Value (FV\displaystyle FV) = 6,00,000\displaystyle 6,00,000 * Time (n\displaystyle n) = 10\displaystyle 10 years * Interest rate (i\displaystyle i) = 10%\displaystyle 10\% p.a. = 0.10\displaystyle 0.10 Substituting the values: Annuity factor=(1.10)10−10.10≈2.593742−10.10=15.93742\text{Annuity factor} = \frac{(1.10)^{10} - 1}{0.10} \approx \frac{2.593742 - 1}{0.10} = 15.93742 A=6,00,00015.93742≈37,647.27A = \frac{6,00,000}{15.93742} \approx 37,647.27 Mathematically, the annual contribution is 37,647\displaystyle 37,647 (Option C). However, the official key marks Option B (37,476\displaystyle 37,476). Hence, **Option B** is the correct answer.

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