Calculate ordinary annuity or present value from interest rate and number of periods using the annuity formula for known cash flow.
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Ordinary Annuity Formula
The calculator uses the ordinary annuity future value relationship. In this setup, the payment is entered in the Present Value 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
- PV = payment amount entered in the Present Value field
- r = interest rate per period, written as a decimal
- n = number of periods
To solve for the payment amount entered in the Present Value field, the calculator rearranges the formula:
- OA = ordinary annuity value
- PV = payment amount needed each period
- r = interest rate per period, written as a decimal
- n = number of periods
If you leave the Ordinary Annuity Value field blank, the calculator finds the future value of the ordinary annuity. If you leave the Present Value field blank, it finds the required periodic payment. The interest rate and number of periods must be entered because this calculator does not solve those two variables by iteration.
Ordinary Annuity Rate and Period Reference
| Payment Timing | Rate to Enter | Periods to Enter |
|---|---|---|
| Monthly payments, annual rate quoted | Annual rate ÷ 12 | Years × 12 |
| Quarterly payments, annual rate quoted | Annual rate ÷ 4 | Years × 4 |
| Annual payments | Annual rate | Number of years |
Use a rate and period count that match the payment frequency.
| Input | Meaning in the Calculator | Example |
|---|---|---|
| Present Value | 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.
- Present Value: 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 $1,067.90.
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.
