Annuities

Read this text on annuities, a type of investment in which regular payments are made over multiple periods. It discusses the present and future value of annuities and how to calculate them.

An annuity is a type of multi-period investment where a certain principal is deposited, and then regular payments are made over the course of the investment. The payments are all a fixed size. For example, a car loan may be an annuity: To get the car, you are given a loan to buy the car. In return, you make an initial payment (down payment), and then you make payments each month of a fixed amount. There is still an interest rate implicitly charged in the loan. The sum of all the payments will be greater than the loan amount, just as with a regular loan, but the payment schedule is spread out over time.

Suppose you are the bank that makes the car loan. There are three advantages to making the loan an annuity. The first is that there is a regular, known cash flow. You know how much money you'll be getting from the loan and when you'll be getting it. The second is that it should be easier for the person you are loaning to to repay because they are not expected to pay one large amount at once. The third reason why banks like to make annuity loans is that it helps them monitor the financial health of the debtor. If the debtor starts missing payments, the bank knows immediately that there is a problem, and they could potentially amend the loan to make it better for both parties.

Similar advantages apply to the debtor. There are predictable payments, and paying smaller amounts over multiple periods may be advantageous over paying the whole loan plus interest and fees back at once.

Since annuities, by definition, extend over multiple periods, there are different types of annuities based on when the payments are made. The three types are:

Annuity-due: Payments are made at the beginning of the period. For example, if a period is one month, payments are made on the first of each month.
Ordinary Annuity: Payments are made at the end of the period. If the period is one month, this means that payments are made on the 28th/30th/31st of each month. Mortgage payments are usually ordinary annuities.
Perpetuities: Payments continue forever. This is much rarer than the first two types.

Key Points

Annuities have payments of a fixed size paid at regular intervals.
There are three types of annuities: annuities-due, ordinary annuities, and perpetuities.
Annuities help both the creditor and debtor have predictable cash flows, and it spreads payments of the investment out over time.

Term

Period – the length of time during which interest accrues.

Source: Boundless Finance, https://ftp.worldpossible.org/endless/eos-rachel/RACHEL/RACHEL/modules/en-boundless-static/www.boundless.com/finance/textbooks/boundless-finance-textbook/the-time-value-of-money-5/annuities-57/index.html
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