Mathematics for FinanceMTP June 24 Series IQuestion 1407 of 512
All Questions

How much money is required to be invested every year as to accumulate Rs.6,00,000\displaystyle 6,00,000 at the end of 10 years, 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 c — 37,647\displaystyle 37,647

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

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. 6,00,000\displaystyle \text{Rs. }6,00,000 * 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: 6,00,000=A×(1.10)10−10.106,00,000 = A \times \frac{(1.10)^{10} - 1}{0.10} First, let's calculate (1.10)10\displaystyle (1.10)^{10}: (1.10)10≈2.59374246(1.10)^{10} \approx 2.59374246 Now substitute this back: 6,00,000=A×2.59374246−10.106,00,000 = A \times \frac{2.59374246 - 1}{0.10} 6,00,000=A×1.593742460.106,00,000 = A \times \frac{1.59374246}{0.10} 6,00,000=15.9374246A6,00,000 = 15.9374246 A Solving for A\displaystyle A: A=6,00,00015.9374246≈37,647.23A = \frac{6,00,000}{15.9374246} \approx 37,647.23 Thus, the amount required to be invested every year is approximately Rs. 37,647\displaystyle \text{Rs. }37,647. Hence, **Option C** is the correct answer.

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If Rs. 1,000\displaystyle \text{Rs. }1,000 be invested at interest rate of 5%\displaystyle 5\% and the interest be added to the principal every 10\displaystyle 10 years, then the number in years in which it will amount to Rs. 2,000\displaystyle \text{Rs. }2,000 is:

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