Calculator Inputs
Example Data Table
| Periodic Payment | Years | Annual Discount | Compounding | Payment Frequency | Type | Growth | Deferred Periods | Approx. PV |
|---|---|---|---|---|---|---|---|---|
| 1,000.00 | 5 | 6% | Monthly | Monthly | Ordinary | 0% | 0 | 51,725.56 |
| 2,500.00 | 10 | 8% | Quarterly | Quarterly | Due | 2% | 2 | 22,000+ depending on exact rounding |
The first row is a fixed annuity example. The second row shows a growing due annuity with a short payment delay.
Formula Used
This calculator first converts the annual discount rate into an effective rate per payment period. It then discounts every payment individually and sums the discounted values. That direct approach supports ordinary annuities, annuities due, growing payments, and deferred starts.
Effective periodic discount rate:
For discrete compounding:
i = (1 + r / m)m / f - 1
For continuous compounding:
i = er / f - 1
Payment growth per period:
gp = (1 + g)1 / f - 1
Level ordinary annuity present value:
PV = PMT × [1 - (1 + i)-n] / i
Growing ordinary annuity present value:
PV = PMT × [1 - ((1 + gp) / (1 + i))n] / (i - gp)
Annuity due adjustment:
PVdue = PVordinary × (1 + i)
Deferred annuity adjustment:
PVdeferred = PV / (1 + i)d,
where d is the number of deferred payment periods.
How to Use This Calculator
- Enter the payment made each period.
- Choose the total number of years.
- Set the annual discount rate.
- Enter annual payment growth if payments increase over time.
- Select the compounding frequency for the discount rate.
- Select how often payments occur.
- Choose ordinary or due timing.
- Set deferred periods if payments start later.
- Press the calculate button to show the result above the form.
- Review the graph, discounted schedule, and export files if needed.
FAQs
1. What does present value mean for an annuity?
Present value is today’s worth of all future annuity payments after discounting them by the selected rate. It shows what those payments are worth right now.
2. What is the difference between ordinary and due annuities?
An ordinary annuity pays at the end of each period. An annuity due pays at the beginning of each period, so its present value is usually higher.
3. Why does payment frequency matter?
Payment frequency changes both the number of payments and the effective discount rate per payment period. Monthly and annual annuities with the same annual rate do not have the same present value.
4. What does deferred period mean?
Deferred periods delay the first payment. Because money received later is discounted more heavily, a deferred annuity usually has a lower present value than an immediate one.
5. Can this calculator handle growing payments?
Yes. Enter a positive annual payment growth rate to model rising payments, or a negative rate above minus one hundred percent to model declining payments.
6. What happens when the discount rate is zero?
With a zero discount rate, future payments are not discounted. Present value becomes the simple sum of payments, adjusted only for timing and growth.
7. Why is the graph useful?
The graph helps you see how each payment contributes to value and how total discounted value builds over time. It makes timing effects easier to interpret.
8. What do the CSV and PDF exports include?
They export the key summary metrics and the full discounted cash flow schedule. That makes reporting, checking, and sharing results much easier.