Future Value of an Annuity, FVA

Definition

In general terms, an annuity is a series of equal cash inflows or outflows made at fixed intervals. A series of coupon payments of a fixed-rate bond is an example of an annuity. So, the future value of an annuity (FVA) is a value at a specific date in the future based on a regular cash flow amount and interest rate.

Formula

Depending on the moment the regular payment is made, annuities can be classified as two types: an ordinary annuity is when cash flow comes in at the end of a relevant period. Its future value can be calculated as follows:

future-value-of-an-ordinary-annuity-1

Here P is payment or cash flow per period, I represents the interest rate per period, and N is the number of periods.

If a regular payment is made at the beginning of the relevant period, we have an example of an annuity due. The formula to find its future value is shown below.

future-value-of-an-annuity-due-2

In turn, the equation describing the relationship between the future value of an ordinary annuity and annuity due is as follows:

future-value-of-an-annuity-due-3

Examples

Let’s assume that someone invests $1,000 each year for 5 years at an annual interest rate of 7.5%. If $1,000 is invested at the end of each year, we have an ordinary annuity. The future values of each cash flow are schematically presented in the chart below.

FV-Ordinary-Annuity-1

The first $1,000 invested at the end of the first year will earn interest during 4 years, and its future value will be $1,335.47. The next $1,000 invested at the end of the second year will earn interest during 3 years and will have a future value of $1,242.30. The same calculations are made for the other cash flows.

FV1 = $1,000 (1+0,075)4 = $1,335.47

FV2 = $1,000 (1+0,075)3 = $1,242.30

FV3 = $1,000 (1+0,075)2 = $1,155.63

FV4 = $1,000 (1+0,075)1 = $1,075.00

FV5 = $1,000 (1+0,075)0 = $1,000.00

Thus, the total future value of all cash flows will be $5,808.39. We can also get the same result using the formula of future value of an ordinary annuity mentioned above.

FVA-1

Let’s assume that $1,000 is invested at the beginning of each year. Under such a scenario, we have the annuity due, and its cash flows will be as follows:

FV-Annuity-Deu-2

The first payment made at the beginning of the first year will earn interest during 5 years, and its future value will reach $1,435.63. The second $1,000 invested at the beginning of the second year will earn interest during 4 years, etc.

FV0 = $1,000 (1+0,075)5 = $1,435.63

FV1 = $1,000 (1+0,075)4 = $1,335.47

FV2 = $1,000 (1+0,075)3 = $1,242.30

FV3 = $1,000 (1+0,075)2 = $1,155.63

FV4 = $1,000 (1+0,075)1 = $1,075.00

The total future value of cash flows will reach $6,244.02 at the end of the fifth year. The same amount can be calculated using the formula of future value of an annuity due.

FVA-2

FVA-3

Calculator and Tables

You can also calculate the future value of an annuity using our online calculator or tables.