**Future value of annuity payment = [FV (R)] ÷ [(1 + R)**^{n}** – 1]**

FV = future value

R = rate for period

N = # of periods

Future value of annuity formula helps to determine the cashflows from investments when the future value is available. As you may alreadyknow that a series of periodic payments is known as an annuity. A simple annuitypayment formula can only be used when the present value of the investmentis known.

That’s why to determine the future value of investment there must be a particular equation to calculate the future value of the annuity. Now one may clearly understand the difference in both concepts. For more understanding, I would like to say one more thing. Both PV of annuity payment and *FV of annuity payment* not only differ by name but there is a huge mathematical difference alongside calculation approach. Moreover, the application of both concepts in real life differs in various aspects.

To understand the difference in *present value* and *futurevalue* let’s consider an example. If you get a loan from a bank and thenpayback with monthly installments at a rate of 5% now here the original loanamount will be present value.

While on the other side, if you open a savings account witha particular amount and want to know the ending balance say after 5 years thenthis will be the future value. In the former example, the balance is decreasingover the time that’s why the present value of the annuity payment formula willbe used. While with later example the balance is increasing that’s why the futurevalue of the annuity payment formula is used.

## How the future value of the annuity payment formula induced

Future value of annuity payment formula is used to derivethe FV of annuity payment formula.

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

The formula above can then be rearranged to solve forpayment;

P = FV ÷ [ {(1 + r)^{n} – 1} ÷ r]

Now if we multiply the equation with the reciprocal of theright part of the equation then we will get the equation which is available ontop of this page.

### FV of annuity payment formula example

Let’s assume that Tim & Stewart Co. is looking to investin a project (saving account) and requested the consulting firm to calculatethe saving amount (monthly payments to account) to reach an ending balance of$7,500 after 4 years. The interest rate per month for this saving account is2.3%.

Now putting values in the annuity payments formula;

P = [$7,500 × (0.023)] ÷ [(1 + 0.023)^{48} – 1]

P = $87.18 _{per month}

One thing must be noted here, we use monthly rate that’s whywe converted the number of periods to months (i.e. 4 ×12 = 48). Therefore theresulted figure also comes in per month basis.

P = $1,046.16 _{per year}

You may notice that we use the ordinary annuity formula forthis calculation. That’s because the first cash flow was not immediate ratherit was 1 month later. If the cash flow is immediate at the starting time ofinvestment, then the Future value of annuity due formula will be used.