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Annuity Calculator: Present Value, Future Value and Payment
Work with a level series of payments: find what it is worth today, what it grows to, or the payment needed to hit a target. Choose payments at the end or the start of each period.
Ordinary annuity and annuity due
An annuity is a series of equal payments at regular intervals. In an ordinary annuity each payment arrives at the end of its period, which is how most loan repayments, bond coupons and many pensions work. In an annuity due each payment arrives at the start, as with rent, insurance premiums and many lease payments. Because every payment of an annuity due sits one period closer to the future (or earlier in the timeline), its present and future values are those of the ordinary annuity multiplied by (1 + i).
This page covers the financial-maths annuity: a level stream with a known rate and length. It is not a quote for an insurance product, which also depends on mortality, fees and the terms the provider offers.
The formulas
With i as the rate per period, n as the number of payments and PMT as the level payment:
- Present value (ordinary):
PV = PMT × (1 − (1 + i)−n) ÷ i - Future value (ordinary):
FV = PMT × ((1 + i)n − 1) ÷ i - Annuity due: multiply either result by
(1 + i). - Payment: divide the target by the matching factor above.
If the rate is zero, both factors reduce to n, so the value is just the payment times the number of payments. A worked check: 1,000 paid at the end of each year for 10 years at 5% has a present value of 7,721.73 and a future value of 12,577.89.
When to use each mode
- Present value answers how much you need now to fund a stream of withdrawals, or what a stream of future payments is worth today.
- Future value answers what regular savings will grow to.
- Payment for a present value is the loan formula: the payment that repays a balance. The result matches the loan calculator for the same terms.
- Payment for a future value is a savings or sinking-fund target.
Limits to keep in mind
The model needs a constant rate and level payments. It does not index payments to inflation, add taxes or fees, or model the chance that you outlive the fund. A fixed rate over twenty years or more is a strong assumption, so run a lower rate as well. Another common slip is entering a yearly rate while the payments are monthly: the calculator divides the annual rate by the number of payments a year, so leave the rate as the annual figure and change only the payment frequency. Compare an ordinary annuity with an annuity due on the same terms to see how much timing alone is worth. The related present value calculator and future value calculator handle single lump sums.
Worked example
What lump sum today would fund 1,500 a month for 15 years if the money earns 4.8% a year?
Inputs
| What do you want to find? | Present value of a payment stream |
|---|---|
| Payment per period | 1500 |
| Annual interest or discount rate | 4.8 % |
| Payments per year | Monthly |
| Number of years | 15 |
| Payments are made at the | End of each period (ordinary annuity) |
Result
180 payments of 1,500.00, at the end of each period, at 4.8% a year.
| Payment per period | 1,500.00 |
|---|---|
| Number of payments | 180 |
| Present value | 192,205.57 |
| Future value | 394,306.80 |
| Total of all payments | 270,000.00 |
| Growth in the future value beyond payments | 124,306.80 |
Yearly balance
| Year | Paid out | Balance at year end |
|---|---|---|
| Year 1 | 18,000.00 | 183,235.81 |
| Year 2 | 18,000.00 | 173,825.90 |
| Year 3 | 18,000.00 | 163,954.24 |
| Year 4 | 18,000.00 | 153,598.18 |
| Year 5 | 18,000.00 | 142,733.95 |
| Year 6 | 18,000.00 | 131,336.61 |
| Year 7 | 18,000.00 | 119,380.00 |
| Year 8 | 18,000.00 | 106,836.67 |
| Year 9 | 18,000.00 | 93,677.84 |
| Year 10 | 18,000.00 | 79,873.30 |
| Year 11 | 18,000.00 | 65,391.37 |
| Year 12 | 18,000.00 | 50,198.81 |
- Rate per period = annual rate ÷ payments per year. The table shows the balance left in a fund that pays this stream out, ending at zero.
Financial disclaimer: Results are estimates for planning and education. They are not financial, tax or legal advice. Fees, taxes, rates and rules vary by lender, product and country, so confirm figures with your provider or a qualified adviser before making decisions.
Frequently asked questions
What is the difference between an ordinary annuity and an annuity due?
An ordinary annuity pays at the end of each period and an annuity due pays at the start. The due version is worth more by a factor of one plus the periodic rate.
How do I calculate the present value of an annuity?
Multiply the payment by one minus the periodic growth factor raised to the negative number of payments, then divide by the periodic rate.
Can this work out a loan payment?
Yes. Choose "Payment for a given present value" with the loan amount as the target, and set the payments per year and term to match the loan.
What happens at a zero rate?
The factors equal the number of payments, so present and future value both equal the payment times the number of payments.
Is this the same as buying an annuity from an insurer?
No. An insurer prices an annuity using life expectancy, costs and its own product terms, so quotes differ from this pure interest calculation.
Related calculators
References and sources
- Standard time-value-of-money texts: present value and future value of ordinary annuities and annuities due.
- Investor.gov (U.S. SEC): background on annuities as financial products. Link