Understanding Annuities

What Are Annuities?

An annuity is a series of equal payments made at regular intervals. These payments can be made weekly, monthly, yearly, or at any other consistent period. Annuities are often used in financial products like pensions, loans, and insurance.

For example:

• Receiving a fixed amount of money every month from a retirement fund.
• Paying a fixed monthly amount for a car loan.

Types of Annuities

• Ordinary Annuity: Payments are made at the end of each period.
• Annuity Due: Payments are made at the beginning of each period.

Calculating Annuities

To calculate the future value or present value of an annuity, you can use specific formulas. These formulas help determine how much the annuity will be worth in the future or what its current value is.

Future Value of an Annuity

The future value of an annuity can be calculated using the formula:

$$FV = P \times \frac{(1 + r)^n - 1}{r}$$

• $FV$: Future Value of the annuity
• $P$: Payment amount per period
• $r$: Interest rate per period
• $n$: Total number of payments

Present Value of an Annuity

The present value of an annuity can be calculated using the formula:

$$PV = P \times \frac{1 - (1 + r)^{-n}}{r}$$

• $PV$: Present Value of the annuity
• $P$: Payment amount per period
• $r$: Interest rate per period
• $n$: Total number of payments

Examples

Example 1: Calculating Future Value

Calculate the future value of an annuity with a monthly payment of $200, an annual interest rate of 6% compounded monthly, over 5 years.

Example 2: Calculating Present Value

Calculate the present value of an annuity that pays $500 annually for 10 years, with an annual interest rate of 5%.