Mathematics of FinancePYQ Sept 25Question 4421 of 507
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Suppose you deposit ₹ 1,000 today, ₹ 2,000 after one year from today and 3,000 after two years from today, in a deposit that pays 10% per annum, compounded annually. What is the balance in the deposit at the end of two year in just after deposit of ₹ 3,000?

Options

A6,000
B6,410
C6,600
D6,800
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Correct Answer

Option b6,410

All Options:

  • A6,000
  • B6,410
  • C6,600
  • D6,800

Detailed Solution & Explanation

We need to find the balance at the end of two years, immediately after the third deposit of ₹ 3,000 is made.
Let us find the future value of each deposit at the end of Year 2: 1) First deposit of ₹ 1,000 is made today (Year 0). It will earn interest for 2 years (compounded annually at 10%): FV1=1,000×(1+0.10)2=1,000×1.21=1,210 rupeesFV_1 = 1,000 \times (1 + 0.10)^2 = 1,000 \times 1.21 = 1,210\text{ rupees}
2) Second deposit of ₹ 2,000 is made after one year (Year 1). It will earn interest for 1 year: FV2=2,000×(1+0.10)1=2,000×1.10=2,200 rupeesFV_2 = 2,000 \times (1 + 0.10)^1 = 2,000 \times 1.10 = 2,200\text{ rupees}
3) Third deposit of ₹ 3,000 is made after two years (Year 2). Since we are checking the balance immediately after this deposit, it has earned no interest: FV3=3,000 rupeesFV_3 = 3,000\text{ rupees}
The total balance at the end of Year 2 is: Total Balance=FV1+FV2+FV3=1,210+2,200+3,000=6,410 rupees\text{Total Balance} = FV_1 + FV_2 + FV_3 = 1,210 + 2,200 + 3,000 = 6,410\text{ rupees}
Hence, **Option B** 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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