Ordinary annuity explained: Formula and how it works

Ordinary annuities are common payment structures found in financial products from car loans to retirement funds. They appear in many everyday financial decisions because they rely on predictable payments that are easy to plan around. Understanding how these payments work helps you evaluate costs and compare options so you can make informed decisions about long-term commitments. 

Here, you’ll discover what an ordinary annuity is and how it differs from an annuity due. You’ll also learn how to calculate ordinary annuity present and future values and find out why these calculations are central to smart financial planning.

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What is an ordinary annuity?

An ordinary annuity is a recurring payment made at the end of a determined interval — like monthly, quarterly, or annually, depending on the contract. This end-of-period timing is what separates it from other payment structures and shapes how each calculation works.

Ordinary annuities can refer to payments made or received. In some cases, a person makes a payment toward a product or service. The individual might be paying down a car loan or a mortgage. An investor might be contributing to a retirement account or receiving retirement income from an annuity that pays at the end of each period.

People sometimes confuse an ordinary annuity with an annuity due. If annuity payments occur at the beginning of each period, the structure is an annuity due. This distinction is important as an ordinary annuity and an annuity due follow slightly different formulas and distinct schedules.

How ordinary annuities work: Payment timing explained

Money in an ordinary annuity either earns or costs money over time. A person investing in a retirement fund will accumulate earnings, and an individual with a loan will pay interest fees. The longer an investor invests, the more they earn; and the longer a borrower pays off a loan, the more they pay in interest. 

Here’s a deeper dive on a few of the central implications of this timing structure.

Interest compounding

Compound interest is essentially interest earning interest over time. Each period, the interest rate applies to both the original amount and prior interest. This process can make savings grow faster. Each payment invested earlier has more time to grow, creating a much larger sum over time than simple interest would. 

For borrowers, compound interest increases the total cost of a loan. Longer schedules mean more periods for interest to accrue. 

Number of periods

The total number of periods refers to the number of payments in the ordinary annuity. For example, a three-year car loan with monthly payments has 36 periods. A 10-year loan with annual payments has 10 periods. 

Present value of an ordinary annuity

The present value (PV) of an ordinary annuity refers to today’s value of future payments, either on an investment or debt. This calculation helps you compare a stream of income to a lump sum and can also help you understand the true cost of a loan.

To calculate the present value, investors must know the rate of return (discount rate), and borrowers need to know the interest rate. With this information, investors can project how much they’ll earn over time, and borrowers can estimate how much they’ll pay toward interest. 

Present value is a particularly important concept for retirement investors. They may find that investing in regular annuity payments over time will not drive the same returns as investing a lump sum today. Money often carries more value in the present because it can be invested immediately and begin compounding.

Other retirement investors may prefer the guaranteed income annuity payments provide. Predictable cash flows can support long-term planning and reduce uncertainty. This consistency offers peace of mind, even if the present value is lower than a lump sum. 

Present value of ordinary annuity formula

The ordinary annuity present value formula is: 

‍PVord = pmt × (1 - ( 1 + r )-n ) / r

Where:

• PV = Present value (what it’s worth today)
• pmt = Payment amount (how much you’ll receive each period)
•  r = Interest rate (the rate applied per period)
• n = Number of periods (how many payments you’ll receive)
• ord = Ordinary annuity

Consider an ordinary annuity calculation with the following variables:

Payment amount (pmt): $1,000

Annual interest rate: 5%

Number of periods: 10 years

For simplicity, the example uses years instead of months. This annuity pays $1,000 annually for 10 years. There’s a 5% compound interest rate annually. Using the present value formula, we can calculate the present value (PV) of the ordinary annuity:

PVord = 1000 × (1 − ( 1 + 0.05)−10​) / 0.05 = $7,722

‍As a purchaser, you may pay a little more than the present value for this annuity to cover fees and commissions. But the PV calculation gives you a starting point to determine the appropriate price. 

Common mistakes when calculating present value

The following are common mistakes people make when using the present value formula for an ordinary annuity:

• Rate vs. period mismatch: Be sure to use the interest or return rate corresponding to the period you’re calculating. Using an annual interest rate with monthly payments will distort the result and lead to inaccurate present value calculations. 
• Calculating annuity due: Using the wrong annuity formula can produce a present value that is either too high or too low. An annuity due requires an adjustment because payments occur at the beginning of each period. Be sure to use the formula for ordinary annuity present value shown above.

Ordinary annuity vs. annuity due: Key differences

An annuity due works almost identically to an ordinary annuity, but payments occur at the beginning of each period instead of at the end. For that reason, the present value calculation is different (same shorthand here, except due means annuity due):

PVdue ​= (pmt × (1 − ( 1 + r )⁻ⁿ ) / r) × (1 + r)

The PVord and PVdue formulas are similar, but to calculate PVdue,  you multiply the ordinary annuity result by one period of interest (1 + r), which increases the present value. 

Here’s an example of how the difference in calculations affects the present value of an annuity due versus an ordinary annuity:

• Payment amount: $1,000
• Interest rate: 5%
• Number of periods: 10 years

PVord = 1000 × (1 − ( 1 + 0.05)⁻¹⁰​) / 0.05 = $7,722

PVdue = 1000 × (1 − ( 1 + 0.05)⁻¹⁰​) / 0.05 × 1.05 = PVord × 1.05 = $8,108

In the example, the annuity due’s present value is $386 more than the ordinary annuity’s. So you, as the purchaser, should pay less for the ordinary annuity. 

Ordinary annuity and annuity due can look like the same concepts, but their payment timing impacts the interest rate applied to each payment and changes how compounding works. 

Value impact for investments

When it comes to investments, the small timing difference between ordinary annuity and annuity due payments can make a significant impact on value. Investors receive annuity due payments earlier — at the beginning of a period — increasing liquidity and allowing more time for compounding. This earlier timing creates more growth potential than receiving funds at the end of the period in an ordinary annuity. 

Common use cases

Annuity due and ordinary annuity structures are often found in similar use cases. For example, someone saving for retirement may choose an annuity that pays at the beginning or end of each period. A landlord could charge a renter at the beginning or end of a month.

Which is better: Annuity due or ordinary annuity?

Either an annuity due or an ordinary annuity can be a best-fit option depending on your financial goals. For someone earning money from an investment, annuity due can be more beneficial as they’ll have more liquid funds up front to reinvest. But for a borrower paying a loan or rental, an ordinary annuity may feel more manageable, as it gives you more time to save before needing to make a payment.

What to consider before using an ordinary annuity

Before you consider using an ordinary annuity, review the following factors to help you evaluate opportunity cost and long-term outcomes.

Time horizon

A time horizon is the length of time that you’ll hold an investment before cashing it out or a loan before paying it off. A long time horizon can mean greater earnings for investors, as returns accrue and compound over time. But for borrowers, a lengthy time horizon increases total interest paid. Shorter repayment periods are often more attractive since they result in paying less overall.

Payment certainty

Payment certainty helps you know the exact amount and timing of each payment. For example, in a payment-certain structure, a person might owe $2,000 in rent on the 30th of each month, or a retiree may receive $1,000 from their retirement account at the end of each quarter. Payment certainty helps borrowers and investors financially plan, projecting how much cash flow they’ll have at any given time.

Opportunity cost

In finance, opportunity cost means choosing one financial structure over another and potentially losing out on the benefits of the structure not selected. Selecting an ordinary annuity may reduce access to a lump sum that could be invested at a higher rate. But choosing the lump sum may reduce predictable income from annuity payments. Make sure to compare present value calculations to help evaluate trade-offs. 

Future value of an ordinary annuity

The future value of an ordinary annuity shows how much the annuity payments will be worth at a later date. This formula helps you calculate how money in an annuity investment will grow or how much you’ll end up owing on a loan. 

Future and present value calculations work together. Present value helps determine what a future investment or debt could be worth now. Future value shows what the investment is worth later. Both help you compare opportunity cost across different financial structures. 

Future value formula for an ordinary annuity

The formula for the future value of an ordinary annuity is:

FVord = pmt x [ ([1 + r]^n – 1) / r]

Where: 

FV = Future value (what it’s worth at a later date)

pmt = Amount of each annuity payment

r = interest or discount rate

n = number of periods

ord = Ordinary annuity

For example, an ordinary annuity with 12 payment periods, a discount rate of 6% per period, and a payment amount of $500 has a future value of $6,167.78, where $6,000 accounts for total payments and $167.78 for total interest. Here’s how it would look:

Payment amount: $500 

Interest rate: 6% 

Number of periods: 12

FVord = 500 × [ (1 + 0.06)^12 – 1] / 0.06 ]

FVord = 500 × [ (1.06)¹² – 1 ] / 0.06 = $6,167.78

Acquire annuities directly with Gainbridge

Ordinary annuities are everywhere, including student loans, mortgage payments, and retirement accounts. This debt-and-investment structure schedules regular payments and distributions for the end of periods, making it easier for investors and borrowers to calculate projected income, interest, and cash-flow scenarios. 

Explore Gainbridge to learn more about how modern fixed annuities are structured, compare current guaranteed rates, and understand how end-of-period payment annuities can support predictable, long-term income planning with products like FastBreak™ or SteadyPace™.

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This article is intended for informational purposes only. It is not intended to provide, and should not be interpreted as, individualized investment, legal, or tax advice. The Gainbridge® digital platform provides informational and educational resources intended only for self-directed purposes.

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