Why is gifting treated as an annuity due rather than an ordinary annuity?

Annuity due vs. ordinary annuity differs by ONE thing: when in the year the payment occurs. Annuity due = start of period. Ordinary annuity = end of period.

For gifting strategies:

The grandparent writes the check on, say, January 5 of each year. So the first gift happens at the start of the planning period — that's an annuity due. Each gift then has one extra year to compound.

Annuity-due FV formula:

The extra $(1 + r)$ factor reflects that every payment gets one additional year of compounding compared to the end-of-year-payment ordinary-annuity case.

Ordinary-annuity FV formula:

This is the standard textbook formula. Used when the payment happens at the END of each year — like bond coupons, salary deferrals into a 401(k) (where contributions are made over time and the convention is end-of-year), or rent payments received.

Comparison for the same parameters:

$PMT = \$19{,}000$, $r = 5\%$, $N = 30$:

The annuity due is $\sim 5\%$ higher (exactly the multiplier $(1 + r)$).

When to use which:

The exam test:

CFA Level III vignettes use phrases like:

• "The first payment is made today" → annuity due
• "The first payment is made one year from now" → ordinary annuity
• "Gifts are made at the start of each year" → annuity due
• "Rents are received at the end of each year" → ordinary annuity

Common mistake:

Forgetting the extra $(1 + r)$ factor in the annuity-due FV is a common error. It's a $5\%$ understatement of the result (if $r = 5\%$), which is often enough to push your answer into a "no" answer-choice band on multiple choice. Always double-check whether the question is asking annuity due or ordinary annuity before computing.