Mathematics of FinanceMCQMTP June 24 Series IQuestion 1530 of 512
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The future value of an annuity of 1500\displaystyle 1500 made annually for 5\displaystyle 5 years at an interest rate of 10%\displaystyle 10\% compounded annually is

Options

A9517.56\displaystyle 9517.56
B9157.65\displaystyle 9157.65
C9715.36\displaystyle 9715.36
D9175.65\displaystyle 9175.65
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Correct Answer

Option b9157.65\displaystyle 9157.65

All Options:

  • A9517.56\displaystyle 9517.56
  • B9157.65\displaystyle 9157.65
  • C9715.36\displaystyle 9715.36
  • D9175.65\displaystyle 9175.65

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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) = 1,500\displaystyle 1,500 * Time (n\displaystyle n) = 5\displaystyle 5 years * Interest rate (i\displaystyle i) = 10%\displaystyle 10\% p.a. = 0.10\displaystyle 0.10 Substituting the values: FV=1,500[(1.10)510.10]FV = 1,500 \left[ \frac{(1.10)^5 - 1}{0.10} \right] Using (1.10)5=1.61051\displaystyle (1.10)^5 = 1.61051: FV=1,500×6.1051=9,157.65FV = 1,500 \times 6.1051 = 9,157.65 This matches Option B (9157.65\displaystyle 9157.65). 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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