Calculator Inputs
Example Data Table
| Example | Payment | Rate | Years | Payments/Year | Compounds/Year | Timing | Present Value |
|---|---|---|---|---|---|---|---|
| Basic ordinary annuity | $1,000.00 | 5.00% | 5 | 1 | 1 | Ordinary | $4,329.48 |
| Monthly annuity due | $500.00 | 7.20% | 10 | 12 | 12 | Due | Higher than ordinary because payments arrive sooner |
| Growing annuity | $800.00 | 9.00% | 8 | 4 | 12 | Ordinary | Depends on the growth and discount relationship |
Formula Used
1) Convert the annual discount rate to a payment-period rate
i = (1 + r / m)^(m / p) - 1
2) Convert annual payment growth to a payment-period growth rate
g = (1 + growth)^(1 / p) - 1
3) Present value of an ordinary growing annuity
PV = PMT × [1 - ((1 + g) / (1 + i))^n] / (i - g)
4) Special case when the periodic discount rate equals the periodic growth rate
PV = PMT × n / (1 + i)
5) Timing and deferment adjustment
PVadjusted = PVordinary × TimingMultiplier ÷ (1 + i)^d
Here, PMT is the first payment amount, n is the number of payments, i is the periodic discount rate, g is the periodic growth rate, and d is the number of deferred periods.
How to Use This Calculator
- Enter the amount of the first annuity payment.
- Provide the annual discount rate used for present value calculations.
- Enter the annuity term in years.
- Choose how many payments happen each year.
- Choose how many times interest compounds each year.
- Add annual payment growth if the annuity increases over time.
- Use deferred periods when payments start later than usual.
- Select ordinary annuity or annuity due based on timing.
- Pick the desired currency symbol and decimal precision.
- Click the calculate button, then review the result, table, graph, and export buttons.
FAQs
1) What does present value of an annuity mean?
It is the value today of a stream of future payments after discounting each payment back to the present using the chosen rate.
2) What is the difference between ordinary annuity and annuity due?
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 do payment frequency and compounding frequency both matter?
They can differ. The calculator first converts the annual discount rate into an effective rate for each payment period, which affects every discounted cash flow.
4) Can this calculator handle growing annuities?
Yes. Enter a positive or negative annual payment growth rate. The tool converts that annual growth into a payment-period growth rate automatically.
5) What are deferred periods used for?
Deferred periods postpone the entire payment stream. This lowers present value because the money arrives later and is discounted for additional periods.
6) Why can total cash flow exceed present value?
Total cash flow is the simple sum of all nominal payments. Present value is smaller because future payments are discounted to reflect time value of money.
7) What happens when growth equals the discount rate?
The standard growing-annuity formula becomes unstable, so the calculator switches to the matching-rate shortcut formula for a reliable result.
8) Can I export the result for reports or sharing?
Yes. After calculation, use the CSV or PDF buttons to download a summary and the full discounted cash flow schedule.