What do you call the type of annuity in which the payments extend over an indefinite length of time

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What Is an Ordinary Annuity?

An ordinary annuity is a series of equal payments made at the end of consecutive periods over a fixed length of time. While the payments in an ordinary annuity can be made as frequently as every week, in practice they are generally made monthly, quarterly, semi-annually, or annually. The opposite of an ordinary annuity is an annuity due, in which payments are made at the beginning of each period. These two series of payments are not the same as the financial product known as an annuity, though they are related.

Key Takeaways

• An ordinary annuity is a series of regular payments made at the end of each period, such as monthly or quarterly.
• In an annuity due, by contrast, payments are made at the beginning of each period.
• Consistent quarterly stock dividends are one example of an ordinary annuity; monthly rent is an example of an annuity due.

What's an Ordinary Annuity?

How an Ordinary Annuity Works

Examples of ordinary annuities are interest payments from bonds, which are generally made semiannually, and quarterly dividends from a stock that has maintained stable payout levels for years. The present value of an ordinary annuity is largely dependent on the prevailing interest rate.

Because of the time value of money, rising interest rates reduce the present value of an ordinary annuity, while declining interest rates increase its present value. This is because the value of the annuity is based on the return your money could earn elsewhere. If you can get a higher interest rate somewhere else, the value of the annuity in question goes down.

Present Value of an Ordinary Annuity Example

The present value formula for an ordinary annuity takes into account three variables. They are as follows:

• PMT = the period cash payment
• r = the interest rate per period
• n = the total number of periods

Given these variables, the present value of an ordinary annuity is:

• Present Value = PMT x ((1 - (1 + r) ^ -n ) / r)

For example, if an ordinary annuity pays $50,000 per year for five years and the interest rate is 7%, the present value would be:

• Present Value = $50,000 x ((1 - (1 + 0.07) ^ -5) / 0.07) = $205,010

An ordinary annuity will have a lower present value than an annuity due, all else being equal.

Present Value of an Annuity Due Example

Recall that with an ordinary annuity, the investor receives the payment at the end of the time period. That stands in contrast to an annuity due, in which the investor receives the payment at the beginning of the period. A common example is rent, where the renter typically pays the landlord in advance for the month ahead. This difference in payment timing affects the value of the annuity. The formula for an annuity due is as follows:

• Present Value of Annuity Due = PMT + PMT x ((1 - (1 + r) ^ -(n-1) / r)

If the annuity in the above example was instead an annuity due, its present value would be calculated as:

• Present Value of Annuity Due = $50,000 + $50,000 x ((1 - (1 + 0.07) ^ -(5-1) / 0.07) = $219,360.

All else being equal, an annuity due is always worth more than an ordinary annuity, because the money is received earlier.

What Is Annuity Due?

An annuity due is an annuity whose payment is due immediately at the beginning of each period. A common example of an annuity due payment is rent, as landlords often require payment upon the start of a new month as opposed to collecting it after the renter has enjoyed the benefits of the apartment for an entire month.

Key Takeaways

• Annuity due is an annuity whose payment is due immediately at the beginning of each period.
• Annuity due can be contrasted with an ordinary annuity where payments are made at the end of each period.
• A common example of an annuity due payment is rent paid at the beginning of each month.
• An example of an ordinary annuity includes loans, such as mortgages.
• The present and future value formulas for an annuity due differ slightly from those for an ordinary annuity as they account for the differences in when payments are made.

What Is An Annuity?

How Annuity Due Works

An annuity due requires payments made at the beginning, as opposed to the end, of each annuity period. Annuity due payments received by an individual legally represent an asset. Meanwhile, the individual paying the annuity due has a legal debt liability requiring periodic payments.

Because a series of annuity due payments reflect a number of future cash inflows or outflows, the payer or recipient of the funds may wish to calculate the entire value of the annuity while factoring in the time value of money. One can accomplish this by using present value calculations.

A present value table for an annuity due has the projected interest rate across the top of the table and the number of periods as the left-most column. The intersecting cell between the appropriate interest rate and the number of periods represents the present value multiplier. Finding the product between one annuity due payment and the present value multiplier yields the present value of the cash flow.

A whole life annuity due is a financial product sold by insurance companies that require annuity payments at the beginning of each monthly, quarterly, or annual period, as opposed to at the end of the period. This is a type of annuity that will provide the holder with payments during the distribution period for as long as they live. After the annuitant passes on, the insurance company retains any funds remaining.

Income payments from an annuity are taxed as ordinary income.

Annuity Due vs. Ordinary Annuity

An annuity due payment is a recurring issuance of money upon the beginning of a period. Alternatively, an ordinary annuity payment is a recurring issuance of money at the end of a period. Contracts and business agreements outline this payment, and it is based on when the benefit is received. When paying for an expense, the beneficiary pays an annuity due payment before receiving the benefit, while the beneficiary makes ordinary due payments after the benefit has occurred.

The timing of an annuity payment is critical based on opportunity costs. The collector of the payment may invest an annuity due payment collected at the beginning of the month to generate interest or capital gains. This is why an annuity due is more beneficial for the recipient as they have the potential to use funds faster. Alternatively, individuals paying an annuity due lose out on the opportunity to use the funds for an entire period. Those paying annuities thus tend to prefer ordinary annuities.

Examples of Annuity Due

An annuity due may arise due to any recurring obligation. Many monthly bills, such as rent, car payments, and cellphone payments, are annuities due because the beneficiary must pay at the beginning of the billing period. Insurance expenses are typically annuities due as the insurer requires payment at the start of each coverage period. Annuity due situations also typically arise relating to saving for retirement or putting money aside for a specific purpose.

How to Calculate the Value of an Annuity Due

The present and future values of an annuity due can be calculated using slight modifications to the present value and future value of an ordinary annuity.

Present Value of an Annuity Due

The present value of an annuity due tells us the current value of a series of expected annuity payments. In other words, it shows what the future total to be paid is worth now.

Calculating the present value of an annuity due is similar to calculating the present value of an ordinary annuity. However, there are subtle differences to account for when annuity payments are due. For an annuity due, payments are made at the beginning of the interval, and for an ordinary annuity, payments are made at the end of a period. The formula for the present value of an annuity due is:

With:

• C = Cash flows per period
• i = interest rate
• n = number of payments

Let's look at an example of the present value of an annuity due. Suppose you are a beneficiary designated to immediately receive $1000 each year for 10 years, earning an annual interest rate of 3%. You want to know how much the stream of payments is worth to you today. Based on the present value formula, the present value is $8,786.11.

Future Value of an Annuity Due

The future value of an annuity due shows us the end value of a series of expected payments or the value at a future date.

Just as there are differences in how the present value is calculated for an ordinary annuity and an annuity due, there are also differences in how the future value of money is calculated for an ordinary annuity and an annuity due. The future value of an annuity due is calculated as:

Using the same example, we calculate that the future value of the stream of income payments to be $11,807.80.

Annuity Due FAQs

Which Is Better, Ordinary Annuity or Annuity Due?

Whether an ordinary annuity or an annuity due is better depends on whether you are the payee or payer. As a payee, an annuity due is often preferred because you receive payment up front for a specific term, allowing you to use the funds immediately and enjoy a higher present value than that of an ordinary annuity. As a payer, an ordinary annuity might be favorable as you make your payment at the end of the term, rather than the beginning. You are able to use those funds for the entire period before paying.

Often, you are not afforded the option to choose. For example, insurance premiums are an example of an annuity due, with premium payments due at the beginning of the covered period. A car payment is an example of an ordinary annuity, with payments due at the end of the covered period.

What Is an Immediate Annuity?

An immediate annuity is an account, funded with a lump sum deposit, that generates an immediate stream of income payments. The income can be for a stated amount (e.g., $1,000/month), a stated period (e.g., 10 years), or a lifetime.

How Do You Calculate the Future Value of an Annuity Due?

The future value of an annuity due is calculated using the formula:

where

• C = cash flows per period
• i = interest rate
• n = number of payments

What Does Annuity Mean?

An annuity is an insurance product designed to generate payments immediately or in the future to the annuity owner or a designated payee. The account holder either makes a lump sum payment or a series of payments into the annuity and can either receive an immediate stream of income or defer receiving payments until some time in the future, usually after an accumulation period where the account earns interest tax-deferred.

What Happens When an Annuity Expires?

Once an annuity expires, the contract terminates and no future payments are made. The contractual obligation is fulfilled, with no further duties owed from either party.

The Bottom Line

An annuity due is an annuity with payment due or made at the beginning of the payment interval. In contrast, an ordinary annuity generates payments at the end of the period. As a result, the method for calculating the present and future values differ. A common example of an annuity due is rent payments made to a landlord, and a common example of an ordinary annuity includes mortgage payments made to a lender. Depending on whether you are the payer or payee, the annuity due might be a better option.

What do you call the type of annuity in which the payments in extend over an infinite length of time?

What do you call to the type of annuity which payments begin at the end of definite times?

How do you call the annuity where the payment interval is also the same as the interest period?

What is the type of annuity in which the payment interval is not the same as the interest period?