Mathematics of FinanceMCQPYQ Jan. 21Question 1447 of 512
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The present value of an annuity immediate is the same as

Options

AAnnuity regular for (n1)\displaystyle (n - 1) year plus the initial receipt in the beg. of the period.
BAnnuity regular for (n1)\displaystyle (n - 1) years
CAnnuity regular for (n+1)\displaystyle (n + 1) years
DAnnuity regular for (n+1)\displaystyle (n + 1) years plus an initial receipt in the beginning of the period.
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Correct Answer

Option aAnnuity regular for (n1)\displaystyle (n - 1) year plus the initial receipt in the beg. of the period.

All Options:

  • AAnnuity regular for (n1)\displaystyle (n - 1) year plus the initial receipt in the beg. of the period.
  • BAnnuity regular for (n1)\displaystyle (n - 1) years
  • CAnnuity regular for (n+1)\displaystyle (n + 1) years
  • DAnnuity regular for (n+1)\displaystyle (n + 1) years plus an initial receipt in the beginning of the period.

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Detailed Solution & Explanation

An **annuity immediate** (or ordinary annuity) has payments made at the end of each period. An **annuity due** (or annuity regular) has payments made at the beginning of each period. The present value of an annuity due of n\displaystyle n years is mathematically equivalent to the present value of an ordinary annuity for (n1)\displaystyle (n-1) years plus a single cash flow received immediately at time t=0\displaystyle t=0: PVdue(n,i)=C+PVordinary(n1,i)PV_{\text{due}}(n, i) = C + PV_{\text{ordinary}}(n-1, i) This is described in Option A: "Annuity regular for (n1)\displaystyle (n - 1) year plus the initial receipt in the beginning of the period." 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.

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