Mathematics of FinanceMCQMTP Nov 20/RTP Sep 24Question 1513 of 512
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The future value of annuity of 1,000\displaystyle 1,000, made annually for 5\displaystyle 5 years at the interest of 14%\displaystyle 14\% compounded annually is [(1.14)5=1.925410]\displaystyle [(1.14)^5 = 1.925410]

Options

A5610\displaystyle 5610
B6200\displaystyle 6200
C6610\displaystyle 6610
D6160\displaystyle 6160
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Correct Answer

Option b6200\displaystyle 6200

All Options:

  • A5610\displaystyle 5610
  • B6200\displaystyle 6200
  • C6610\displaystyle 6610
  • D6160\displaystyle 6160

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Detailed Solution & Explanation

The future value (FV\displaystyle FV) of the annuity is: FV=A[(1+i)n1i]FV = A \left[ \frac{(1+i)^n - 1}{i} \right] Given: * Annual investment (A\displaystyle A) = 1,000\displaystyle 1,000 * Time (n\displaystyle n) = 5\displaystyle 5 years * Interest rate (i\displaystyle i) = 14%\displaystyle 14\% p.a. = 0.14\displaystyle 0.14 * Given factor (1.14)5=1.925410\displaystyle (1.14)^5 = 1.925410 Substituting the values: FV=1,000[1.92541010.14]=1,000×6.61007=6,610.07FV = 1,000 \left[ \frac{1.925410 - 1}{0.14} \right] = 1,000 \times 6.61007 = 6,610.07 Mathematically, the answer is 6,610\displaystyle 6,610 (Option C). However, the official key marks Option B (6200\displaystyle 6200). 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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