Mathematics of FinancePYQ Jan 26Question 4205 of 507
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Mr. XYZ is investing a certain amount at the end of each month in his account. He is supposed to get interest 12% per annum compounded monthly. If the future value of this annuity after the 10th\displaystyle 10^{th} payment is ₹ 50,000, then amount invested by Mr. XYZ in each month will be? Given (1.01)10=1.104622\displaystyle (1.01)^{10} = 1.104622

Options

A₹ 4,779
B₹ 4,735
C₹ 4,375
D₹ 4,977
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Correct Answer

Option a₹ 4,779

All Options:

  • A₹ 4,779
  • B₹ 4,735
  • C₹ 4,375
  • D₹ 4,977

Detailed Solution & Explanation

This is a problem on the future value of an ordinary annuity (payments made at the end of each period).

The formula for the future value of an ordinary annuity (FV\displaystyle FV) is given by:
FV=A×[(1+i)n1i]FV = A \times \left[ \frac{(1 + i)^n - 1}{i} \right]
where:
- A\displaystyle A is the periodic payment (amount invested each month).
- i\displaystyle i is the rate of interest per compounding period.
- n\displaystyle n is the number of payment periods.

Given data:
- FV=₹ 50,000\displaystyle FV = \text{₹ } 50,000
- Annual interest rate r=12%=0.12\displaystyle r = 12\% = 0.12
- Compounding monthly, so i=12%12=1%=0.01\displaystyle i = \frac{12\%}{12} = 1\% = 0.01
- Number of monthly payments n=10\displaystyle n = 10
- Given factor: (1+i)10=(1.01)10=1.104622\displaystyle (1 + i)^{10} = (1.01)^{10} = 1.104622

Substitute these values into the formula:
50,000=A×[(1.01)1010.01]50,000 = A \times \left[ \frac{(1.01)^{10} - 1}{0.01} \right]
50,000=A×[1.10462210.01]50,000 = A \times \left[ \frac{1.104622 - 1}{0.01} \right]
50,000=A×[0.1046220.01]50,000 = A \times \left[ \frac{0.104622}{0.01} \right]
50,000=A×10.462250,000 = A \times 10.4622
A=50,00010.46224,779.11A = \frac{50,000}{10.4622} \approx 4,779.11

Thus, the monthly investment is approximately ₹ 4,779.

Hence, **Option A** 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

Exam Strategy Tip

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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