For the same periodic payment, rate and number of periods, the present value of an annuity due compared with that of an immediate (ordinary) annuity is: (A) equal to it (B) it multiplied by (1 + i) (C) it divided by (1 + i) (D) it multiplied by (1 + i)^n

Question

Accepted Answer

In an **annuity due** every payment is made one full period earlier than in the corresponding immediate annuity, so each is discounted for one *fewer* period — i.e. each present value is larger by a factor $(1+i)$. Summing, the whole present value scales the same way:
$$P_{	ext{due}}=C\left[\frac{1-(1+i)^{-n}}{i}ight](1+i)=P(1+i).$$
Hence option **(B)** is correct.

**Why the other options are wrong:**
- (A) *equal to it* — false; earlier payments are worth more, so the due value is strictly larger (for $i>0$).
- (C) *divided by $(1+i)$* — this discounts further, the wrong direction; earlier payments need *less* discounting, not more. …

Q.For the same periodic payment, rate and number of periods, the present value of an annuity due compared with that of an immediate (ordinary) annuity is: (A) equal to it (B) it multiplied by (1 + i) (C) it divided by (1 + i) (D) it multiplied by (1 + i)^n

Concept understanding — Present Value of an Annuity

Q.For the same periodic payment, rate and number of periods, the present value of an annuity due compared with that of an immediate (ordinary) annuity is: (A) equal to it (B) it multiplied by (1 + i) (C) it divided by (1 + i) (D) it multiplied by (1 + i)^n

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