Ordinary Annuity Calculator
This tool calculates the Future Value (FV) and Present Value (PV) of an ordinary annuity. An ordinary annuity involves a series of equal payments made at the end of each period, with interest compounding at the end of each period as well.
Enter the payment amount, the annual interest rate, the compounding/payment frequency, and the total number of years. The calculator will determine the total value of these payments at a future date (FV) or their equivalent lump-sum value today (PV). Ensure inputs are valid and non-negative.
Input Parameters
Understanding Ordinary Annuities & Formulas
What is an Ordinary Annuity?
An ordinary annuity is a sequence of equal payments made at the end of consecutive periods over a fixed length of time. Common examples include regular deposits to a savings account, monthly mortgage payments (though loan payment calculation is typically the inverse), or regular payouts from a pension fund.
The key characteristic of an ordinary annuity is that payments are made at the *end* of each period, and interest is compounded at the *end* of each period.
Future Value (FV) of an Ordinary Annuity
The future value of an annuity is the total accumulated amount of the payments and interest earned on those payments up to the end of the contract term. It tells you how much your savings will grow to, or the total value of a stream of payments at a future point.
The formula for the Future Value of an Ordinary Annuity is:
FV = P × [ ((1 + i)ⁿ - 1) / i ]
Where:
- P = Payment amount per period
- i = Interest rate per period (Annual Rate / Number of Compounding Periods per Year)
- n = Total number of periods (Number of Years × Number of Compounding Periods per Year)
Present Value (PV) of an Ordinary Annuity
The present value of an annuity is the lump-sum amount needed today that is equivalent to a series of future annuity payments, given a specific rate of return or discount rate. It tells you how much a future stream of income is worth right now, or the initial principal amount of a loan being paid off by annuity payments.
The formula for the Present Value of an Ordinary Annuity is:
PV = P × [ (1 - (1 + i)⁻ⁿ) / i ]
Where:
- P = Payment amount per period
- i = Interest rate per period
- n = Total number of periods
This formula essentially discounts each future payment back to its value at the start of the first period and sums them up.
Ordinary Annuity Examples
Click on an example to see the scenario and inputs:
Example 1: Retirement Savings (Future Value)
Scenario: You save $500 at the end of each month for 30 years. Your investment earns an average annual interest rate of 7%, compounded monthly. What is the future value of your retirement savings?
Inputs:
- Payment Amount (P) = $500
- Annual Interest Rate = 7%
- Compounding/Payment Frequency = Monthly (12 times/year)
- Number of Years = 30
Use the calculator with these inputs to find the Future Value.
Example 2: Value of a Payout (Present Value)
Scenario: You are offered a structured settlement that pays you $1,000 at the end of each month for the next 5 years. Assuming a discount rate of 4% annual interest, compounded monthly, what is the present value of this settlement today?
Inputs:
- Payment Amount (P) = $1,000
- Annual Interest Rate = 4%
- Compounding/Payment Frequency = Monthly (12 times/year)
- Number of Years = 5
Use the calculator with these inputs to find the Present Value.
Example 3: College Fund Savings (Future Value)
Scenario: Your parents deposited $200 at the end of each quarter into a college savings plan for 18 years. The fund earned an average annual interest rate of 5%, compounded quarterly. How much is the fund worth when you turn 18?
Inputs:
- Payment Amount (P) = $200
- Annual Interest Rate = 5%
- Compounding/Payment Frequency = Quarterly (4 times/year)
- Number of Years = 18
Use the calculator with these inputs to find the Future Value.
Example 4: Lottery Annuity Payout (Present Value)
Scenario: You win a lottery that pays you $50,000 at the end of each year for 20 years. If the current market interest rate for such payouts is 3% per year, compounded annually, what is the lump-sum cash value of your winnings today?
Inputs:
- Payment Amount (P) = $50,000
- Annual Interest Rate = 3%
- Compounding/Payment Frequency = Annually (1 time/year)
- Number of Years = 20
Use the calculator with these inputs to find the Present Value.
Example 5: Funding an Investment Payout (Present Value)
Scenario: You want to set up an investment that will pay your child $3,000 at the end of every six months for 10 years, starting six months from now. If the investment can earn an average of 6% annual interest, compounded semi-annually, how much money do you need to invest today?
Inputs:
- Payment Amount (P) = $3,000
- Annual Interest Rate = 6%
- Compounding/Payment Frequency = Semi-Annually (2 times/year)
- Number of Years = 10
Use the calculator with these inputs to find the Present Value.
Example 6: Saving for a Car Down Payment (Future Value)
Scenario: You decide to save $300 at the end of each week for the next 3 years for a car down payment. Your high-yield savings account offers 4% annual interest, compounded weekly. How much will you have saved in total?
Inputs:
- Payment Amount (P) = $300
- Annual Interest Rate = 4%
- Compounding/Payment Frequency = Weekly (52 times/year)
- Number of Years = 3
Use the calculator with these inputs to find the Future Value.
Example 7: Value of an Inheritance Payout (Present Value)
Scenario: You are to receive an inheritance payout of $5,000 at the end of each quarter for the next 7 years. If you could otherwise invest money today at an annual rate of 2%, compounded quarterly, what is the present value of your inheritance?
Inputs:
- Payment Amount (P) = $5,000
- Annual Interest Rate = 2%
- Compounding/Payment Frequency = Quarterly (4 times/year)
- Number of Years = 7
Use the calculator with these inputs to find the Present Value.
Example 8: Funding a Pension (Present Value)
Scenario: A company needs to determine how much money it must set aside today to fund a pension that will pay an employee $2,000 at the end of each month for 25 years after they retire. The company's investments are expected to earn 5% annual interest, compounded monthly.
Inputs:
- Payment Amount (P) = $2,000
- Annual Interest Rate = 5%
- Compounding/Payment Frequency = Monthly (12 times/year)
- Number of Years = 25
Use the calculator with these inputs to find the Present Value (the lump sum needed today).
Example 9: Value of Bond Interest Payments (Present Value)
Scenario: A bond will pay its holder $50 in interest at the end of each year for 15 years (these are called coupon payments). If the required rate of return (yield) for similar bonds is 2.5% per year, compounded annually, what is the present value of these interest payments?
Inputs:
- Payment Amount (P) = $50
- Annual Interest Rate = 2.5%
- Compounding/Payment Frequency = Annually (1 time/year)
- Number of Years = 15
Use the calculator with these inputs to find the Present Value (of the interest stream). Note: The bond's face value repayment at maturity is a separate lump sum calculation.
Example 10: Lump Sum vs. Payout Decision (Present Value)
Scenario: You won $100,000 and can either take a lump sum of $85,000 today or receive $1,000 at the end of each month for 10 years. If you can earn 6% annual interest, compounded monthly, on your investments, which option is financially better today?
Inputs for the Payout:
- Payment Amount (P) = $1,000
- Annual Interest Rate = 6%
- Compounding/Payment Frequency = Monthly (12 times/year)
- Number of Years = 10
Use the calculator with these inputs to find the Present Value of the payout stream. Compare this PV to the $85,000 lump sum to decide.
Frequently Asked Questions about Ordinary Annuities
1. What is the definition of an ordinary annuity?
An ordinary annuity is a series of equal payments made at fixed intervals (periods), where each payment occurs at the *end* of the period, and interest is compounded at the end of each period as well.
2. How is an ordinary annuity different from an annuity due?
The key difference is the timing of payments. In an ordinary annuity, payments are made at the *end* of each period. In an annuity due, payments are made at the *beginning* of each period. Annuity due calculations will typically result in higher future and present values because each payment earns interest for one extra period.
3. What does Future Value (FV) of an ordinary annuity represent?
The Future Value is the total worth of the annuity payments at the end of the annuity term. It includes all the periodic payments plus the accumulated compound interest earned over the entire period. It answers questions like "How much will my savings be worth?"
4. What does Present Value (PV) of an ordinary annuity represent?
The Present Value is the single lump-sum amount at the beginning of the annuity term that has the same economic value as the entire stream of future annuity payments, considering a specific interest or discount rate. It answers questions like "How much is this future stream of income worth today?"
5. How do I determine the "Interest Rate per Period (i)" and "Total Periods (n)"?
If you have an annual interest rate and a compounding/payment frequency (e.g., monthly), the interest rate per period (i) is the annual rate divided by the frequency per year (e.g., 5% annual / 12 months = 0.05/12). The total number of periods (n) is the number of years multiplied by the frequency per year (e.g., 10 years * 12 months/year = 120 periods). This calculator handles this conversion for you based on the inputs you provide.
6. What does "compounding frequency" mean?
Compounding frequency refers to how many times per year interest is calculated and added to the principal. For simple annuities, the payment frequency usually matches the compounding frequency (e.g., monthly payments with monthly compounding), which this calculator assumes. A higher compounding frequency (for the same annual rate) can lead to slightly higher earnings over time.
7. Can this calculator be used for loans?
Yes, the Present Value calculation is directly applicable to loans. The PV represents the initial loan principal amount, P is the regular payment, i is the interest rate per period, and n is the number of payments. While this tool calculates PV *given* P, i, and n, loan calculators typically calculate P *given* PV, i, and n (finding the payment needed to pay off a loan amount).
8. What if the interest rate is 0%?
If the interest rate is 0%, there is no compounding. The future value is simply the total sum of all payments (P * n). The present value is also the total sum of all payments (P * n), as future money is not discounted. This calculator includes logic to handle the 0% rate case correctly.
9. What units should I use for the payment amount?
You can use any currency unit (dollars, euros, etc.) for the payment amount. The calculated Future Value and Present Value will be in the same currency unit. Ensure the annual interest rate is entered as a percentage (e.g., 5 for 5%). The time units (Years, Frequency) must be consistent.
10. Is this suitable for complex financial planning?
This calculator provides fundamental ordinary annuity calculations (FV and PV) based on fixed inputs. Real-world financial scenarios can be more complex, involving changing payment amounts, variable interest rates, taxes, fees, or payments made at the start of periods (annuity due). For complex planning, consult a financial advisor or use more sophisticated software.
