Annuities are regular payments made or received over time, like monthly savings or loan payments.

There are two types of annuities, simple annuities and general annuities. The difference is how the interest is calculated.

Simple Annuities

In a simple annuity, the interest period matches the payment period. For example, if payments are made monthly, the interest is also compounded monthly.

Example

You save $100 every month for 3 months. The bank gives you a 6% annual interest rate compounded monthly, which is 0.5% per month (6% ÷ 12).

• After 1 month, you save $100, and no interest is added yet.
• After 2 months, your $100 earns 0.5% interest ($\$100\times 0.005=\$0.50$). Now you have $100.50. You also add another $100, making your total $200.50.
• After 3 months, your $200.50 earns 0.5% interest ($\$200.50\times 0.005\approx \$1.00$). Now you have $201.50. You add another $100, so the total is $301.50.

At the end of 3 months, you will have $301.50.

General Annuities

In a general annuity, the interest period is different from the payment period. For example, payments might be made monthly, but interest is compounded yearly.

Example

You save $100 every month for 3 months, but the bank adds interest only at the end of the year. The annual interest rate is 6%.

• After 1 month, you save $100, and no interest is added yet.
• After 2 months, you have saved $200, but still no interest is added.
• After 3 months, you have saved $300, but the bank hasn’t added any interest yet.

At the end of the year, the bank will add 6% interest to the total amount saved ($\$300\times 0.06=\$18$). So your total at the end of the year will be $318.

Key Points

• In simple annuities, payments and interest periods match.
• In general annuities, payments and interest periods are different.