An annuity is a financial product that provides a stream of income over a set period. They’re often used in retirement planning as a way to generate income from a lump sum investment.

However, there are different ways these payments can be structured, including ordinary annuities and annuities due. While the concept may seem straightforward, the timing of these payments can have an impact on the overall value of the annuity.

## What is an ordinary annuity?

An ordinary annuity involves a series of equal payments made at the end of each period. These periods can be monthly, quarterly or annually, depending on the specific annuity contract.

### How does an ordinary annuity work?

Imagine you invest a lump sum of money into an annuity. The life insurance company holding your contract will then use this money to generate a stream of payments for you.

Over a preset period, you will receive a fixed amount of money at the end of each month or quarter. This fixed payment is calculated based on the initial investment amount, the interest rate offered by the annuity and the total number of payments.

Here’s a breakdown of the factors involved:

• Present value (PV): The initial lump sum you invest in the annuity.
• Payment (PMT): The fixed amount you receive at the end of each period.
• Interest rate (r): The annual rate of return offered by the annuity, expressed as a decimal.
• Number of periods (n): The total number of payments you will receive.

Using these factors, there’s a specific formula to calculate the payment amount (PMT) for an ordinary annuity:

`PMT = (r/12 * PV) / (1 - (1 + r/12)^(-n)`

### Example

Let’s consider an example to illustrate how an ordinary annuity works. Suppose you invest \$100,000 (PV) into an annuity with an interest rate of 5 percent (r) per year for a period of 10 years (n). You’ll receive monthly payments.

Using the formula for ordinary annuity with monthly payments:

`PMT = (r/12 * PV) / (1 - (1 + r/12)^(-n)`
`PMT = (0.05/12 * \$100,000) / (1 - (1 + 0.05/12)^(-120)`
`PMT = \$1,060.66`

So, with monthly payments, you would receive about \$1,060.66 each month for 10 years in an ordinary annuity.

You can also run the annuity payment calculation with Google Sheets or Excel using the PMT function under financial. Here’s how to do it.

## What is an annuity due?

With an annuity due, the initial payment and all subsequent payments are made at the beginning of each payment period. This seemingly minor difference can impact the overall value of the annuity due to the time value of money.

### How does an annuity due work?

Similar to an ordinary annuity, you invest a lump sum with a life insurance company. However, instead of waiting until the end of the month or quarter to receive your first payment, you receive it at the beginning of the period. Subsequent payments are also received at the beginning of each period.

The calculation of the payment amount (PMT) for an annuity due also uses a formula that considers the time value of money.

### Example

Using the same example from the ordinary annuity, let’s calculate the monthly payment amount for an annuity due with a \$100,000 investment (PV), 5 percent annual interest rate (r) and 10-year term (n).

The formula for the payment for an annuity due is slightly different:

`PMT = PV * (r/12 / (1 - (1 + r/12)^(-n)) * (1 / (1 + r/12)))`
`PMT = 100000 * (0.05/12 / (1 - (1 + 0.05/12)^(-120)) * (1 / (1 + 0.05/12)))`

Where:

• Present value (PV): The initial lump sum you invest in the annuity.
• Payment (PMT): The fixed amount you receive at the beginning of each period.
• Interest rate (r): The annual rate of return offered by the annuity, expressed as a decimal.
• Number of periods (n): The total number of payments you will receive.
`PMT = \$1056.25 (rounded to two decimal places)`

As the example shows, the monthly payment for the annuity due is slightly lower (\$1,056.25) compared to the ordinary annuity (\$1,060.66) due to the time value of money and receiving the first payment earlier.

Remember, these are just examples, and the actual payment amounts of an annuity will differ depending on the specific terms of the contract.

## Key differences between an ordinary annuity and an annuity due

While both ordinary annuities and annuities due provide a stream of income, the main difference is the timing of payments. Ordinary annuities pay at the end of each period, while annuity due payments happen at the beginning.

This seemingly small difference in timing can impact the future value of an annuity because of the time value of money. Money received earlier allows it more time to earn interest, potentially leading to a higher future value compared to an ordinary annuity with the same payment amount.

Receiving payments earlier with an annuity due might be seen as a slight advantage.

You can use an online calculator — or a spreadsheet application, such as Microsoft Excel or Google Sheets — to figure both the present and future value of an annuity, so long as you know the interest rate, payment amount and duration. If you use a spreadsheet, look for the PMT function under financials.

## Bottom line

Understanding ordinary annuities and annuities due can help you make informed financial decisions. While the concept may seem straightforward, the timing of payments can make a real difference in the overall value and income stream you receive. There are online tools available to simplify the calculations for both the present and future value of annuities, ordinary or due. These online calculators typically require the interest rate, payment amount and investment duration as inputs.