Why does begin mode change an annuity answer so much?
I understand that beginning-of-period payments are different from end-of-period payments, but I do not have a good intuition for why the value changes. How should I think about this on exam day?
Beginning-of-period payments are more valuable because each cash flow is received or paid one full period earlier. For present value, that means less discounting. For future value, it means one extra period of compounding.
For example, suppose five annual payments of USD 12,000 are discounted at 7 percent:
- Ordinary annuity present value: USD 49,202.
- Annuity due present value: USD 52,647.
The annuity due is larger because every payment is shifted one year closer to the valuation date. A useful check is:
PV annuity due = PV ordinary annuity x (1 + r)
The exam clue is usually wording such as "payments begin immediately" or "first payment is due today." If the first payment is one period from now, ordinary-annuity timing is the default.
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