Mathematics for FinancePYQ June 19Question 1437 of 512
All Questions

Let a person invest a fixed sum at the end of each month in an account paying interest 12%\displaystyle 12\% per year compounded monthly. If the future value of this annuity after the 12th\displaystyle 12^{th} payment is ₹55,000\displaystyle ₹ 55,000 then the amount invested every month is?

Options

A₹4,837\displaystyle ₹ 4,837
B₹4,637\displaystyle ₹ 4,637
C₹4,337\displaystyle ₹ 4,337
D₹3,337\displaystyle ₹ 3,337
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option c — ₹4,337\displaystyle ₹ 4,337

All Options:

  • A₹4,837\displaystyle ₹ 4,837
  • B₹4,637\displaystyle ₹ 4,637
  • C₹4,337\displaystyle ₹ 4,337
  • D₹3,337\displaystyle ₹ 3,337

Detailed Solution & Explanation

Let the fixed sum invested every month be A\displaystyle A. Given parameters: * Future Value of annuity (FV\displaystyle FV) = Rs. 55,000\displaystyle \text{Rs. }55,000 * Nominal Interest Rate (r\displaystyle r) = 12%\displaystyle 12\% p.a. * Compounding Frequency (m\displaystyle m) = 12\displaystyle 12 (compounded monthly) * Monthly Interest Rate (i\displaystyle i) = 12%12=1%=0.01\displaystyle \frac{12\%}{12} = 1\% = 0.01 * Number of payments (n\displaystyle n) = 12\displaystyle 12 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: 55,000=A×(1.01)12−10.0155,000 = A \times \frac{(1.01)^{12} - 1}{0.01} First, let's calculate (1.01)12\displaystyle (1.01)^{12}: (1.01)12≈1.126825(1.01)^{12} \approx 1.126825 Substituting this back: 55,000=A×1.126825−10.0155,000 = A \times \frac{1.126825 - 1}{0.01} 55,000=A×0.1268250.0155,000 = A \times \frac{0.126825}{0.01} 55,000=12.6825A55,000 = 12.6825 A Solving for A\displaystyle A: A=55,00012.6825≈4,336.68A = \frac{55,000}{12.6825} \approx 4,336.68 Thus, the monthly investment is approximately Rs. 4,337\displaystyle \text{Rs. }4,337. Hence, **Option C** is the correct answer.

Key Concepts to Understand

More Questions from Mathematics for Finance

Ready to Master Mathematics for Finance?

Practice all 512 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free