Mathematics of FinancePYQ May 25Question 4320 of 507
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How much approximate amount should you save annually to accumulate ₹ 20,00,000 by the end of 12 years, if the saving earns an interest of 14 percent compound annually? [Given that (1.14)12=4.8179\displaystyle (1.14)^{12} = 4.8179]

Options

A₹ 4,15,118
B₹ 5,23,848
C₹ 73,339
D₹ 1,11,200
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Correct Answer

Option c₹ 73,339

All Options:

  • A₹ 4,15,118
  • B₹ 5,23,848
  • C₹ 73,339
  • D₹ 1,11,200

Detailed Solution & Explanation

To find the annual amount to save to accumulate a specific future value, we use the future value of an ordinary annuity formula:
FV=A×[(1+i)n1i]FV = A \times \left[\frac{(1 + i)^n - 1}{i}\right]
Where:
- FV=20,00,000\displaystyle FV = ₹ 20,00,000 (Target accumulated sum)
- n=12 years\displaystyle n = 12 \text{ years} (Duration of savings)
- i=14%=0.14\displaystyle i = 14\% = 0.14 (Annual interest rate)
- A\displaystyle A = Annual savings amount

Substitute the given values into the formula:
2000000=A×[(1.14)1210.14]2000000 = A \times \left[\frac{(1.14)^{12} - 1}{0.14}\right]
We are given that (1.14)12=4.8179\displaystyle (1.14)^{12} = 4.8179. Substituting this value:
2000000=A×[4.817910.14]2000000 = A \times \left[\frac{4.8179 - 1}{0.14}\right]
2000000=A×[3.81790.14]2000000 = A \times \left[\frac{3.8179}{0.14}\right]
2000000=A×27.27072000000 = A \times 27.2707
Now solve for A\displaystyle A:
A=200000027.270773338.75A = \frac{2000000}{27.2707} \approx 73338.75
So the annual savings required is approximately 73,339\displaystyle ₹ 73,339.
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

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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