Mathematics of FinanceMCQMTP May 20Question 1509 of 512
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A person invests $500\displaystyle at the end of each year with a bank which pays interest at $10\% p.a C.I. annually. The amount standing to his credit one year after he has made his yearly investment for the $12^{th}$ time is, Given $(1.1)^{12} = 3.1384$.

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option a — $11,761.36$

All Options:

  • A$11,761.36$
  • B$10,000$
  • C$12,000$
  • Dnone of these

Detailed Solution & Explanation

First, we find the future value of the annuity (FV\displaystyle FV) immediately after the $12^{th\displaystyle \text{th}}$ payment: FV12=A[(1+i)n−1i]FV_{12} = A \left[ (1+i)n−1i\displaystyle \frac{(1+i)^n - 1}{i} \right] Given: * Annual investment (A\displaystyle A) = $500$ * Time (n\displaystyle n) = $12$ years * Interest rate (i\displaystyle i) = $10\%\displaystyle p.a. = $0.10 * Given factor (1.1)12=3.1384\displaystyle (1.1)^12 = 3.1384 Substituting the values: FV12=500[3.1384−10.10]=500×21.384=10,692FV_{12} = 500 \left[ 3.1384−10.10\displaystyle \frac{3.1384 - 1}{0.10} \right] = 500 ×\displaystyle \times 21.384 = 10,692 Since we want the value standing to his credit one year after the $12^{th\displaystyle \text{th}}$ investment, we compound it for one more year: FV=10,692×(1+0.10)=11,761.20FV = 10,692 ×\displaystyle \times (1 + 0.10) = 11,761.20 This is closest to Option A ($11,761.36$). 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

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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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