Financial
Present and future value of an annuity: Ordinary (type 0) vs Annuity Due (type 1)
Value leases, pensions, and savings plans accurately by choosing end-of-period (type = 0) vs beginning-of-period (type = 1) cash flows in PV and FV.
When cash flows happen on Day 1 instead of Month-End
Choose type 0 for payments at each period’s end and type 1 for payments at each period’s beginning. The correct timing follows the actual contract; product names alone do not determine it.
Every payment in an Annuity Due compounds (or discounts) for one fewer period on PV and one extra period on FV—multiplying both Present Value and Future Value by exactly (1 + PeriodicRate).
| Schedule ($500/mo, 6% nominal annual rate, 60 mos) | Ordinary (type = 0) | Annuity Due (type = 1) | Exact Ratio |
|---|---|---|---|
| Present Value (-PV) | 25,862.78 | 25,992.09 | x (1 + 0.005) |
| Future Value (-FV) | 34,885.02 | 35,059.44 | x (1 + 0.005) |
PV and FV formulas with type = 0 vs type = 1
Negate -PV and -FV (or pass negative -Payment) to display positive asset/lease values.
=ROUND(-PV(A2 / 12, B2, C2, 0, 1), 2)Future value of 1st-of-month savings (Annuity Due)
Contributing $500 on the 1st instead of the 30th adds $174.42 in extra interest over 60 months.
=ROUND(-FV(A2 / 12, B2, C2, 0, 1), 2)Inputs and interpretation
This assumes equal payments, a constant periodic rate, a positive integer period count and no fees/taxes or extra principal amounts. AnnualRate/12 assumes a nominal annual rate compounded monthly; an effective annual rate needs a different conversion. The (1+rate) ratio applies to the annuity payment component, with the other present/future lump sums set to zero here. Results are mathematical scenarios, not guaranteed investment returns.
Try the example
Use the original values or change them to test your understanding.