**FV of annuity = P [{(1+r)**^{n}** – 1} ÷ r]**

P = Periodic Payment

r = rate

n = number of periods

Typically, the future value of annuity formulais used to calculate the future value of a rente or annuity which is basicallya series of the periodic payment. There are some built-in assumptions on whichthe annuity formula works while making calculations. Such as the rate does notchange in overall term of investment, the first payment is one period away and lastly,the periodic payments do not change.

If any of the above assumption breaks then you have to calculate the future value of each period cash flow separately during the whole annuity term. Moreover, if the first cash flow is received immediately then you must use the future value of annuity due formula for accurate results.

## Future value of annuity formula illustration

Let’s suppose that a company decides to deposit $10,000 peryear into a bank account for saving purpose for total 5 years term. The veryfirst deposit will take in to effect at the end of the first year. However, if adeposit is required immediately then you have to use the future value ofannuity due formula for calculation. The annual rate of return on this depositaccount is 3%, to calculate the future value after 5 years we will use the equationavailable above;

FV of annuity =$10,000 [{(1 + 0.03)^{5} – 1} ÷ 0.03]

After the 5^{th} year, the futurevalue of an investment will be $53,091.36.

### What was the origin of the future value of annuity formula

Future value of a series of cash flow is known as the futurevalue of an annuity. One can also represent the formula for the future value ofthe annuity as;

= P + P(1+r) + … + P(1+ r)^{n-1}

While if we assume that the payments areconsistent throughout the term, then the common ratio of ** 1+r **can be taken out togive;

=P [{1 – (1 + r)^{n}} ÷ {1 – (1 + r)}]

If we multiply the above equation by ** -1/-1**then the outcome will be the same equation as you can see above on top of thispage.