Calculate the future value of equal end-of-period payments, or the payment needed to reach a target future value.
Ordinary Annuity Formula
The calculator uses the ordinary annuity future value relationship. In this setup, enter the recurring amount in the Periodic payment field; the rate is entered as a percent per period, and payments are assumed to occur at the end of each period.
- OA = ordinary annuity value
- PMT = payment amount entered in the Periodic payment field
- r = interest rate per period, written as a decimal
- n = number of periods
To solve for the payment amount entered in the Periodic payment field, the calculator rearranges the formula:
- OA = ordinary annuity value
- PMT = payment amount needed each period
- r = interest rate per period, written as a decimal
- n = number of periods
Choose Future value or Periodic payment, then enter the required values. The rate and payment count must be entered; these two quantities are not solved by iteration. At a zero interest rate, future value equals payment × number of payments.
Ordinary Annuity Rate and Period Reference
| Payment Timing | Rate to Enter | Periods to Enter |
|---|---|---|
| Monthly payments, nominal annual rate compounded monthly | Annual rate ÷ 12 | Years × 12 |
| Quarterly payments, nominal annual rate compounded quarterly | Annual rate ÷ 4 | Years × 4 |
| Annual payments | Annual rate | Number of years |
Use a rate and period count that match the payment frequency. For an effective annual rate EAR and m payments per year, use ((1 + EAR)^(1/m) − 1) as the periodic decimal rate, rather than EAR ÷ m.
| Input | Meaning in the Calculator | Example |
|---|---|---|
| Periodic payment | Periodic payment amount | $500 paid each month |
| Interest Rate | Rate per period, entered as a percent | 0.5 for 0.5% per month |
| Number of Periods | Total number of payments | 60 monthly payments |
| Ordinary Annuity Value | Future value at the end of the last period | Total accumulated value after 60 months |
Example Problems
Example 1: Find the ordinary annuity value
You deposit $1,000 at the end of each year for 5 years. The interest rate is 6% per year.
- Periodic payment: 1000
- Interest Rate: 6
- Number of Periods: 5
The ordinary annuity value is $5,637.09.
Example 2: Find the required periodic payment
You want an ordinary annuity value of $10,000 after 8 periods. The interest rate is 4% per period.
- Ordinary Annuity Value: 10000
- Interest Rate: 4
- Number of Periods: 8
The required periodic payment is $1,085.28.
FAQs
What is an ordinary annuity?
An ordinary annuity is a series of equal payments made at the end of each period. Common examples include yearly deposits into an investment account or monthly payments made at the end of each month.
How is an ordinary annuity different from an annuity due?
In an ordinary annuity, payments happen at the end of each period. In an annuity due, payments happen at the beginning of each period. An annuity due usually grows to a higher value because each payment earns interest for one extra period.
Why do the interest rate and number of periods need to match?
The rate must match the period length. If payments are monthly, use a monthly interest rate and the total number of months. If payments are yearly, use an annual interest rate and the total number of years.
