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

Options

AAnnuity regular for (n−1)\displaystyle (n - 1) year plus the initial receipt in the beg. of the period.
BAnnuity regular for (n−1)\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 a — Annuity regular for (n−1)\displaystyle (n - 1) year plus the initial receipt in the beg. of the period.

All Options:

  • AAnnuity regular for (n−1)\displaystyle (n - 1) year plus the initial receipt in the beg. of the period.
  • BAnnuity regular for (n−1)\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.

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 (n−1)\displaystyle (n-1) years plus a single cash flow received immediately at time t=0\displaystyle t=0: PVdue(n,i)=C+PVordinary(n−1,i)PV_{\text{due}}(n, i) = C + PV_{\text{ordinary}}(n-1, i) This is described in Option A: "Annuity regular for (n−1)\displaystyle (n - 1) year plus the initial receipt in the beginning of the period." Hence, **Option A** is the correct answer.

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