Mathematics for FinanceMTP Jun 23 Series IQuestion 1517 of 512
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How much money is to be invested every year so to accumulate 3,00,000\displaystyle 3,00,000 at the end of 10\displaystyle 10 years if interest is compounded annually at 10%\displaystyle 10\% rate of interest?

Options

A18823.65\displaystyle 18823.65
B18833.64\displaystyle 18833.64
C18223.60\displaystyle 18223.60
D16823.65\displaystyle 16823.65
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Correct Answer

✅ Option a — 18823.65\displaystyle 18823.65

All Options:

  • A18823.65\displaystyle 18823.65
  • B18833.64\displaystyle 18833.64
  • C18223.60\displaystyle 18223.60
  • D16823.65\displaystyle 16823.65

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) = 3,00,000\displaystyle 3,00,000 * 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=3,00,00015.93742≈18,823.62A = \frac{3,00,000}{15.93742} \approx 18,823.62 Hence, **Option A** is the correct answer.

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