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

Options

A11,761.36\displaystyle 11,761.36
B10,000\displaystyle 10,000
C12,000\displaystyle 12,000
Dnone of these
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Correct Answer

Option a11,761.36\displaystyle 11,761.36

All Options:

  • A11,761.36\displaystyle 11,761.36
  • B10,000\displaystyle 10,000
  • C12,000\displaystyle 12,000
  • Dnone of these

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Detailed Solution & Explanation

First, we find the future value of the annuity (FV\displaystyle FV) immediately after the 12th\displaystyle 12^{\text{th}} payment: FV12=A[(1+i)n1i]FV_{12} = A \left[ \frac{(1+i)^n - 1}{i} \right] Given: * Annual investment (A\displaystyle A) = 500\displaystyle 500 * Time (n\displaystyle n) = 12\displaystyle 12 years * Interest rate (i\displaystyle i) = 10%\displaystyle 10\% p.a. = 0.10\displaystyle 0.10 * Given factor (1.1)12=3.1384\displaystyle (1.1)^12 = 3.1384 Substituting the values: FV12=500[3.138410.10]=500×21.384=10,692FV_{12} = 500 \left[ \frac{3.1384 - 1}{0.10} \right] = 500 \times 21.384 = 10,692 Since we want the value standing to his credit one year after the 12th\displaystyle 12^{\text{th}} investment, we compound it for one more year: FV=10,692×(1+0.10)=11,761.20FV = 10,692 \times (1 + 0.10) = 11,761.20 This is closest to Option A (11,761.36\displaystyle 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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