What type of annuity is illustrated when the interest conversion or compounding period is unequal or not same as the payment interval?

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.

Fixed vs. variable annuities

In a fixed annuity, the insurance company guarantees the principal and a minimum rate of interest. In other words, as long as the insurance company is financially sound, the money you have in a fixed annuity will grow and will not drop in value. The growth of the annuity’s value and/or the benefits paid may be fixed at a dollar amount or by an interest rate, or they may grow by a specified formula. The growth of the annuity’s value and/or the benefits paid does not depend directly or entirely on the performance of the investments the insurance company makes to support the annuity. Some fixed annuities credit a higher interest rate than the minimum, via a policy dividend that may be declared by the company’s board of directors, if the company’s actual investment, expense and mortality experience is more favorable than was expected. Fixed annuities are regulated by state insurance departments.

Money in a variable annuity is invested in a fund—like a mutual fund but one open only to investors in the insurance company’s variable life insurance and variable annuities. The fund has a particular investment objective, and the value of your money in a variable annuity—and the amount of money to be paid out to you—is determined by the investment performance (net of expenses) of that fund. Most variable annuities are structured to offer investors many different fund alternatives. Variable annuities are regulated by state insurance departments and the federal Securities and Exchange Commission.

Types of fixed annuities

An equity-indexed annuity is a type of fixed annuity, but looks like a hybrid. It credits a minimum rate of interest, just as a fixed annuity does, but its value is also based on the performance of a specified stock index—usually computed as a fraction of that index’s total return.

A market-value-adjusted annuity is one that combines two desirable features—the ability to select and fix the time period and interest rate over which your annuity will grow, and the flexibility to withdraw money from the annuity before the end of the time period selected. This withdrawal flexibility is achieved by adjusting the annuity’s value, up or down, to reflect the change in the interest rate “market” (that is, the general level of interest rates) from the start of the selected time period to the time of withdrawal. 

Other types of annuities

All of the following types of annuities are available in fixed or variable forms.

Deferred vs. immediate annuities

A deferred annuity receives premiums and investment changes for payout at a later time. The payout might be a very long time; deferred annuities for retirement can remain in the deferred stage for decades.

An immediate annuity is designed to pay an income one time-period after the immediate annuity is bought. The time period depends on how often the income is to be paid. For example, if the income is monthly, the first payment comes one month after the immediate annuity is bought.

Lifetime vs. fixed period annuities

A fixed period annuity pays an income for a specified period of time, such as ten years. The amount that is paid doesn’t depend on the age (or continued life) of the person who buys the annuity; the payments depend instead on the amount paid into the annuity, the length of the payout period, and (if it’s a fixed annuity) an interest rate that the insurance company believes it can support for the length of the pay-out period.

A lifetime annuity provides income for the remaining life of a person (called the “annuitant”). A variation of lifetime annuities continues income until the second one of two annuitants dies. No other type of financial product can promise to do this. The amount that is paid depends on the age of the annuitant (or ages, if it’s a two-life annuity), the amount paid into the annuity, and (if it’s a fixed annuity) an interest rate that the insurance company believes it can support for the length of the expected pay-out period.

With a “pure” lifetime annuity, the payments stop when the annuitant dies, even if that’s a very short time after they began. Many annuity buyers are uncomfortable at this possibility, so they add a guaranteed period—essentially a fixed period annuity—to their lifetime annuity. With this combination, if you die before the fixed period ends, the income continues to your beneficiaries until the end of that period.

Qualified vs. nonqualified annuities

A qualified annuity is one used to invest and disburse money in a tax-favored retirement plan, such as an IRA or Keogh plan or plans governed by Internal Revenue Code sections, 401(k), 403(b), or 457. Under the terms of the plan, money paid into the annuity (called “premiums” or “contributions”) is not included in taxable income for the year in which it is paid in. All other tax provisions that apply to nonqualified annuities also apply to qualified annuities.

A nonqualified annuity is one purchased separately from, or “outside of,” a tax-favored retirement plan. Investment earnings of all annuities, qualified and non-qualified, are tax-deferred until they are withdrawn; at that point they are treated as taxable income (regardless of whether they came from selling capital at a gain or from dividends).

Single premium vs. flexible premium annuities

A single premium annuity is an annuity funded by a single payment. The payment might be invested for growth for a long period of time—a single premium deferred annuity—or invested for a short time, after which payout begins—a single premium immediate annuity. Single premium annuities are often funded by rollovers or from the sale of an appreciated asset.

A flexible premium annuity is an annuity that is intended to be funded by a series of payments. Flexible premium annuities are only deferred annuities; that is, they are designed to have a significant period of payments into the annuity plus investment growth before any money is withdrawn from them.

What type of annuity is illustrated when the interest conversion or compounding period is unequal or the same as the payment interval?

What is the type of annuity in which the payment interval is not the same as the interest period a general annuity b simple annuity c simple interest D compound interest?

Is the interest conversion or compounding period is equal or the same as the payment interval?

What is an annuity where the payment interval is not the same as the interest period *?