Mathematics of FinanceMCQMTP Jun 23 Series IIQuestion 1525 of 512
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The future value of an annuity of 5,000\displaystyle 5,000 is made annually for 8\displaystyle 8 years at interest rate of 9%\displaystyle 9\% compounded annually. [(1.09)8=1.99256]\displaystyle [(1.09)^8 = 1.99256]

Options

A55,142.22\displaystyle 55,142.22
B66,142.22\displaystyle 66,142.22
C65,532.22\displaystyle 65,532.22
D57,423.22\displaystyle 57,423.22
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Correct Answer

Option b66,142.22\displaystyle 66,142.22

All Options:

  • A55,142.22\displaystyle 55,142.22
  • B66,142.22\displaystyle 66,142.22
  • C65,532.22\displaystyle 65,532.22
  • D57,423.22\displaystyle 57,423.22

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Detailed Solution & Explanation

The future value (FV\displaystyle FV) of an ordinary annuity is: FV=A[(1+i)n1i]FV = A \left[ \frac{(1+i)^n - 1}{i} \right] Given: * Annual investment (A\displaystyle A) = 5,00,000\displaystyle 5,00,000 (represented as 5,000\displaystyle 5,000 in system records) * Time (n\displaystyle n) = 8\displaystyle 8 years * Interest rate (i\displaystyle i) = 9%\displaystyle 9\% p.a. = 0.09\displaystyle 0.09 * Given factor (1.09)8=1.99256\displaystyle (1.09)^8 = 1.99256 Substituting the values: FV=5,000[1.9925610.09]=5,000×11.02844=55,142.22FV = 5,000 \left[ \frac{1.99256 - 1}{0.09} \right] = 5,000 \times 11.02844 = 55,142.22 Mathematically, the future value is 55,142.22\displaystyle 55,142.22 (Option A). However, the official key marks Option B (66,142.22\displaystyle 66,142.22). 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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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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