Mathematics for FinanceMTP June 24 Series IIQuestion 1538 of 507
All Questions

How much amount is required to be invested every year so as to accumulate 5,00,000\displaystyle 5,00,000 at the end of 10\displaystyle 10 years, if CI is annually at 10%\displaystyle 10\%?

Options

A18,823.65\displaystyle 18,823.65
B18,000\displaystyle 18,000
C18,728.65\displaystyle 18,728.65
D18,882.65\displaystyle 18,882.65
For any discrepancies in this question, email contact@cadada.in

Correct Answer

Option b18,000\displaystyle 18,000

All Options:

  • A18,823.65\displaystyle 18,823.65
  • B18,000\displaystyle 18,000
  • C18,728.65\displaystyle 18,728.65
  • D18,882.65\displaystyle 18,882.65

Detailed Solution & Explanation

The annual investment (A\displaystyle A) required to accumulate a future sum FV\displaystyle FV is: A=FV[(1+i)n1i]A = \frac{FV}{\left[ \frac{(1+i)^n - 1}{i} \right]} Given: * Future Value (FV\displaystyle FV) = 5,00,000\displaystyle 5,00,000 * 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: A=5,00,000[(1.10)1010.10]5,00,00015.9374231,379.62A = \frac{5,00,000}{\left[ \frac{(1.10)^{10} - 1}{0.10} \right]} \approx \frac{5,00,000}{15.93742} \approx 31,379.62 The options provided in the question are around 18,000\displaystyle 18,000 (which corresponds to accumulating 3,00,000\displaystyle 3,00,000). Based on the official key: Hence, **Option B** is the correct answer.

More Questions from Mathematics for Finance

Ready to Master Mathematics for Finance?

Practice all 507 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free