Mathematics for FinanceMTP March 21Question 1514 of 512
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Future value of an ordinary annuity

Options

AA(n,i)=A1−(1+i)−ni\displaystyle A(n,i) = A \frac{1 - (1+i)^{-n}}{i}
BA(n,i)=A1−(1+i)−ni\displaystyle A(n,i) = A \frac{1 - (1+i)^{-n}}{i}
CA(n,i)=A(1+i)n−1i\displaystyle A(n,i) = A \frac{(1+i)^n - 1}{i}
DA(n,i)=A(1+i)n−1i\displaystyle A(n,i) = A \frac{(1+i)^n - 1}{i}
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Correct Answer

✅ Option a — A(n,i)=A1−(1+i)−ni\displaystyle A(n,i) = A \frac{1 - (1+i)^{-n}}{i}

All Options:

  • AA(n,i)=A1−(1+i)−ni\displaystyle A(n,i) = A \frac{1 - (1+i)^{-n}}{i}
  • BA(n,i)=A1−(1+i)−ni\displaystyle A(n,i) = A \frac{1 - (1+i)^{-n}}{i}
  • CA(n,i)=A(1+i)n−1i\displaystyle A(n,i) = A \frac{(1+i)^n - 1}{i}
  • DA(n,i)=A(1+i)n−1i\displaystyle A(n,i) = A \frac{(1+i)^n - 1}{i}

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] Based on the options provided: Hence, **Option A** is the correct answer.

Key Concepts to Understand

Annuity

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

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