Key takeaways
- Ordinary annuities pay at the end of a period.
- Annuities due pay in advance, or at the beginning of a period.
- Mortgages and car loans are examples of ordinary annuities.
- Rent and subscription fees are examples of annuities due.
- Because of the difference in payment timing, the present value of an annuity due will be higher than the present value of an ordinary annuity with otherwise equal terms.
What's the difference between an ordinary annuity and an annuity due? Both an ordinary annuity and annuity due are contractually obligated payment series. Where they differ is in the timing of the payment. An ordinary annuity pays in arrears, while an annuity due pays in advance.
Ordinary annuity
What is an ordinary annuity?
An ordinary annuity pays at the end of a period -- so the payment covers the period that has already passed. The period can be any designated time frame, such as a month, quarter, or year.
Note that "the end" of the period could be the first of the month. The date on the calendar is not the relevant point. What's relevant is whether the payment covers the prior month or the following month. The annuity contract will specify this information, but the timing of the first payment can also be an indicator.
A traditional mortgage is an example. Your first mortgage payment is due on the first of the month after you've owned the home for 30 days. That payment is in arrears, which makes the mortgage an ordinary annuity. Car loans work the same way. You begin paying 30 days after the loan funds.
Annuity due
What is an annuity due?
An annuity due is paid at the beginning of the period, such that the payment is made in advance. Rent and lease agreements are examples. Your rent for September is due at the beginning of September -- not the end. Subscription fees for services like Netflix (NFLX 4.17%) and Amazon Prime (AMZN 1.3%) are also annuities due because they are paid ahead of the service period.
Key differences
Ordinary annuity vs. annuity due: Key differences
As noted, the primary difference between an ordinary annuity and an annuity due is whether the payment is made in arrears or in advance. This difference, in turn, affects the annuity's present value.
Understanding present value can help you evaluate an annuity relative to its cost. First, know that the present value of any annuity will be less than the sum of the payments. This is because cash promised in the future is not as valuable as cash in your hand today.
Why? Because you can invest and grow cash on hand -- which you cannot do with cash promised. Present value formulas account for this by using an interest rate to discount those future payments.
The present value of the ordinary annuity formula considers the dollar amount of each payment, the discount rate, and the number of payments. The present value of the annuity due formula uses the same inputs but adjusts for the earlier payment timing.
Mathematically, that adjustment involves multiplying the result by the discount rate plus 1. You can see this by comparing the two present value formulas below. Note that "pmt" equals the payment amount, "r" equals the discount rate, and "n" is the total number of payments.
- Present value of ordinary annuity = pmt [(1–[1/(1+r)^n])/r]
- Present value of annuity due = pmt [(1–[1/(1+r)^n])/r] x (1+r)
The takeaway is that an annuity due will have a higher present value vs. an ordinary annuity if all other factors are the same.
Related investing topics
Which one is better?
Ordinary annuity or annuity due: Which one is better?
Ordinary annuities are better for the payer, while annuities due are better for the payee. In other words, if you are paying the annuity, you'd rather pay later. Paying in arrears allows you to keep your funds invested longer -- or gives you more time to earn them via your paycheck.
If you are receiving annuity income, an annuity due is preferred because you get the money sooner. Assuming monthly payments, an annuity due puts the cash in your hands one month earlier vs. an ordinary annuity.
Ordinary annuity vs. annuity due: FAQs
What is the difference between ordinary annuity and annuity due?
An ordinary annuity differs from an annuity due by the timing of the payments. Ordinary annuity payments are made at the end of a period, which can be monthly, quarterly, or annually. Annuity due payments, on the other hand, are made at the beginning of the period. You pay your credit card bill at the end of the billing cycle, so it's an ordinary annuity. However, you pay rent, subscription fees, and insurance premiums in advance. These are annuities due.
Annuities sold by insurance companies to provide retirement income can be structured as ordinary annuities or annuities due.
What are the four types of annuities?
The four main types of annuities are immediate annuities, deferred annuities, fixed annuities, and variable annuities. Immediate vs. deferred annuities differ in when the payments begin.
An immediate annuity begins producing income right away. A deferred annuity starts generating payments at some future date, with taxes also deferred until that time. You'd purchase an immediate annuity with a lump sum of cash. You can buy a deferred annuity with a single cash payment or a series of payments over time.
Fixed and variable annuities differ in risk and return. Fixed annuities provide income based on a fixed interest rate. They are lower risk because the interest rate and payment amount don't change. Variable annuities produce income based on the performance of sub-accounts, which are usually stock or bond investment funds chosen by the annuitant. These have more return potential than fixed annuities and more risk.
What is considered an ordinary annuity?
An ordinary annuity can be any financial obligation that requires periodic payments made at the end of a period. Mortgages and car loans are ordinary annuities because you pay those in arrears, usually starting 30 or more days after the loan funds.
