Financial Analyst Education Center

Future Value of an Annuity (FVA)

Determining the future value of a cash flow is one of the most important elements in the financial calculations, particularly for those which are based on the idea of time value of money. Annuities are known as a widespread financial instrument, determining the future value of which is an important step for proper and profitable investment decision.

In simple words, an annuity is a set of equal cash flows arising at equal periods. However, the future value of an annuity will depend on whether the regular payment has been made at the beginning or at the end of each period. If the cash flow (regular payment) occurs at the beginning of each period, it is called as ”Annuity Due”. On the other hand, regular payment made at the end of each period means that this is an “Ordinary Annuity”. To better understand the situation, let’s take a look at this example.

Let’s assume an annuity for which an investor is going to place annually $1,000 on a saving account for five years. The bank offers annual interest rate of 5%. The future value of this annuity will depend on whether the payment is made at the beginning or at the end of each year.

If an investor makes regular payment at the beginning of each year (annuity due), the future value of all cash flows will be similar to what is shown below.

Future Value of an Annuity Due

The future value of each cash flow can be calculated using the following formula.

Future Value Formula

where PV – present value of a cash flow;

i – interest rate or required rate of return;

N – number of periods.

The present value of each cash flow is.

FV1 = $1,000/(1+0.05)5 = $1,276.28

FV2 = $1,000/(1+0.05)4 = $1,215.51

FV3 = $1,000/(1+0.05)3 = $1,157.63

FV4 = $1,000/(1+0.05)2 = $1,102.50

FV5 = $1,000/(1+0.05)1 = $1,050

The first $1,000 is placed to the savings account at the beginning of first year and will be compounded for all the 5 years. The second payment of $1,000 will be compounded for 4 year, etc. Thus, the future value of an annuity will be the sum of all five cash flows which is $5,801.91.

FVA = $1,276.28+$1,215.51+$1,157.63+$1,102.50+$1,050=$5,801.91

We can also calculate the future value of an annuity due using the following formula.

Future Value of an Annuity Due Formula

where A – the amount of regular payment;

i – interest rate;

N – number of periods.

Putting the data from the example above in the formula, we get $ 5,801.91.

If an investor decides to place money in the savings account at the end of each period (ordinary annuity), the future value of all cash flows will be similar to what is shown below.

Future Value of an Ordinary Annuity

In this case, the first $1,000 will be placed at the end of first year (at point 1), and will be compounded for 4 years, the second $1,000 will be compounded for 3 years, etc. Finally, investor will place the last $1,000 at the end of 5th year 5 and this amount won’t be compounded at all.

Thus, the present value of each cash flow will be:

FV1 = $1,000/(1+0.05)4 = $1,215.51

FV2 = $1,000/(1+0.05)3 = $1,157.63

FV3 = $1,000/(1+0.05)2 = $1,102.50

FV4 = $1,000/(1+0.05)1 = $1,050

FV5 = $1,000/(1+0.05)0 = $1,000

The future value of the annuity is the sum of all cash flows that is $5,525.63.

FVA = $1,215.51+$1,157.63+$1,102.50+$1,050+$1,000=$5,525.63

The future value of this ordinary annuity can be calculated using the following formula as well:

Future Value of an Ordinary Annuity Formula

Using the data from the example above we get $5,525.63; this can be confirmed by the previous calculation as well.

As shown by the above calculations, the future value of an annuity can vary significantly depending on whether the regular payment is made at the beginning or at the end of each period. For example, the lessor will be in an advantageous position to receive advance payments from the lessee. On the other hand, the lessee is benefitted more by paying rent payments at the end of each month, rather than at the beginning. Thus, this factor must be taken into account in the financial calculations which estimate available investment opportunities.

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