Mathematics of FinanceMCQMTP May 18Question 1484 of 512
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Future value of Ordinary Annuity

Options

AA(n,i)=A[(1+i)n−1i]\displaystyle A(n,i) = A \left[ \frac{(1+i)^n - 1}{i} \right]
BA(n,i)=A[(1+i)ni]\displaystyle A(n,i) = A \left[ \frac{(1+i)^n}{i} \right]
CA(n,i)=A[1−(1+i)ni]\displaystyle A(n,i) = A \left[ \frac{1 - (1+i)^n}{i} \right]
DA(n,i)=A[(1+i)n−1i(1+i)]\displaystyle A(n,i) = A \left[ \frac{(1+i)^n - 1}{i(1+i)} \right]
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Correct Answer

✅ Option a — A(n,i)=A[(1+i)n−1i]\displaystyle A(n,i) = A \left[ \frac{(1+i)^n - 1}{i} \right]

All Options:

  • AA(n,i)=A[(1+i)n−1i]\displaystyle A(n,i) = A \left[ \frac{(1+i)^n - 1}{i} \right]
  • BA(n,i)=A[(1+i)ni]\displaystyle A(n,i) = A \left[ \frac{(1+i)^n}{i} \right]
  • CA(n,i)=A[1−(1+i)ni]\displaystyle A(n,i) = A \left[ \frac{1 - (1+i)^n}{i} \right]
  • DA(n,i)=A[(1+i)n−1i(1+i)]\displaystyle A(n,i) = A \left[ \frac{(1+i)^n - 1}{i(1+i)} \right]

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Detailed Solution & Explanation

The standard formula for the Future Value of an Ordinary Annuity (A(n,i)\displaystyle A(n,i)) with regular payments of A\displaystyle A, interest rate i\displaystyle i per period, and n\displaystyle n periods is: A(n,i)=A[(1+i)n−1i]A(n,i) = A \left[ \frac{(1+i)^n - 1}{i} \right] This matches Option A. 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

Exam Strategy Tip

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.

Key Concepts to Understand

Annuity

A sequence of equal periodic payments made at equal intervals of time.

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