Mathematics of FinanceMCQPYQ June 19Question 1437 of 512
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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

A4,837\displaystyle ₹ 4,837
B4,637\displaystyle ₹ 4,637
C4,337\displaystyle ₹ 4,337
D3,337\displaystyle ₹ 3,337
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Correct Answer

Option c4,337\displaystyle ₹ 4,337

All Options:

  • A4,837\displaystyle ₹ 4,837
  • B4,637\displaystyle ₹ 4,637
  • C4,337\displaystyle ₹ 4,337
  • D3,337\displaystyle ₹ 3,337

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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)n1iFV = A \times \frac{(1+i)^n - 1}{i} Substituting the values: 55,000=A×(1.01)1210.0155,000 = A \times \frac{(1.01)^{12} - 1}{0.01} First, let's calculate (1.01)12\displaystyle (1.01)^{12}: (1.01)121.126825(1.01)^{12} \approx 1.126825 Substituting this back: 55,000=A×1.12682510.0155,000 = 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=55,00012.68254,336.68A = \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.

About This Chapter: Mathematics of Finance

Paper

Paper 3: Quantitative Aptitude

Weightage

12-16 Marks

Key Topics

Simple & Compound Interest, Annuity, Perpetuity

The most important mathematical chapter in the entire syllabus. It covers Simple Interest (SI), Compound Interest (CI), Nominal vs Effective rates, Present and Future Value, Annuities (Ordinary and Due), Sinking Funds, and Perpetuities. The concepts learned here are applied heavily in CA Intermediate and Final.

View Official ICAI Syllabus

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Guaranteed 12-16 marks. Master your calculator! Learn the 'GT' and compound interest M+/M- tricks to solve annuity questions in 10 seconds without writing long formulas.

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