# Is Future Value of Annuity Due Offer Reasonable Outcomes to Make Decisions

Future Value of Annuity Due = (1 + r) × P [{(1 + r)n – 1} ÷ r]

P = Periodic Payment
r = rate
n = number of periods

Future value of annuity due formula is utilized to calculatethe amount one will receive at maturity of an investment having a series ofpayments and the first payment is received instantly. The only differencebetween an ordinary annuity and annuity due is the first instant paymentthat’s why annuity due is also known as instant annuity sometimes.

The future value of an annuity due is used with a slightly different approach in the professional world as opposed to the present value of an annuity due. For instance, if an individual is planning to buy an annuity from another person where the first payment is made instantly, he may like to know the amount for which he should buy it.

In such a case, the present value of annuity due formula will be used to calculate the PV of the investment. On the other side if an individual wants to determine the balance at the end of the investment say after 4 years, where the first payment is made today. In such a case the future value of an annuity due will be used to get the maturity amount at the end of annuity.

## How Future value of annuity due formula derived

The future value of annuity due formula can be induced byusing various approaches. We can use the Future value formula at firststep to then reach the required result. As we know that;

FV = PV (1 + r)n

Now we will use the present value of annuity due formulaand then multiply it with (1 + r)n to get us;

FV = (1 + r) × P [{1 – (1 + r)-n} ÷ r]

From here, maybe you notice that we can convert aboveequation to just the formula shown at the top of this page by just multiplyingit with (1 + r)n.

Another way to calculate the future value of an annuitydue is by comparing cash flows from ordinary annuity and annuity due. Theannuity due cash flows can be calculated by using this formula;

Annuity due cash flows = P(1 +r) + P(1 + r)2 … P(1 + r)n

On the other side the cash flows for an ordinary annuity canbe calculated by using the following formula;

Cash flows for ordinary annuity = P + P(1 + r) … P(1 + r)n – 1

If you notice, annuity due formula for cash flows can beconverted to ordinary annuity cash flows formula by just factoring out (1 +r) from it. Thus we can also determine the future value of an annuitydue by simply multiplying (1 + r) with ordinary annuity cashflow formula which is shown at top of this page.

### Future value of annuity due example

We will continue with the example we discuss earlier wherethe maturity of the investment comes after 4 years. The amount deposited inthat interest-bearing account is \$1,500 on per annum basis however, the depositis made for today’s date. The rate of return is 4.3% annually, now calculatethe future value of an annuity due to this data.

FV of annuity due = (1 + 0.043) × \$1,500 [ { (1 + 0.043)4– 1 } ÷ 0.043]

FV of an annuity due after 4 years will be = \$6,673.34