Future Value of Annuity Due Formula – Steps to Follow and How it is Computed

Annuity due and its future value are important factors to consider before you plan to invest your hard-earned money into any plans.

Annuity due is defined as a series of recurring equal payments which are due to be paid at the beginning of regular intervals such as monthly, quarterly, or annual payment cycles. Some of the common examples of Annuity due are EMIs, rent, insurance premiums, etc. Annuity due differs from an ordinary annuity, as in the case of an ordinary annuity the payments are made at the end of each cycle instead of at the beginning. An insurance plan that pays annuity due would make the interest payment at the beginning of a period to the policyholder or beneficiary. If you want to calculate the future value of the annuity due, you can use the annuity due formula.

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Future value of the annuity due formula

Future Value = P x {(1 + r) n – 1) / r} x (1 + r)

Where:

P = Value of each annuity payment

r = rate of interest

n = number of payment instances

Let us understand the calculations better with an example. Mr. P is planning to deposit an amount of INR 10,000 annually for a period of 10 years. The market rate of interest is going at 5% annually. In such a scenario

P = 10,000

r = 5%

n = 10

Future Value = 10000 x {(1 + 5%) 10 – 1) / 5%} x (1 + 5%)

= 10000 x {(1 + .05) 10 – 1) / .05} x (1 + .05)

= 10000 x {(1.05)10 -1) / .05} x (1.05)

= 1,32,067.87

As demonstrated by the example, the future value of the annuity due would be higher than the one accumulated through an ordinary annuity. This happens due to the extra compound interest for paying the annuity due at the beginning of the payment term.

The steps that have to be followed are mentioned below:

• The amount which is required to be paid each period has to be decided. The payment amount has to be equal to the periodic payments. These are called P
• In the next step, you have to verify the rate of interest that is charged on the basis of the rates that are available in the market. It is represented as r
• The formula for finding out r, which is the annualized interest rate or number of periodic payments each year
• It is the rate of interest that the investor receives after an investment of the money in the market
• Now, the total number of periods is derived by simply multiplying the number of years with that of the number of periodic payments
• By using the above-mentioned formula, you can calculate the future value of an annuity.

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How is the Future Annuity Due Formula Computed?

In the first method, you will be able to multiply (1 + r) n by the present value of the annuity due. The current value of the annuity due formula is (1 + r) * P {1 – (1 + r) – n} / r.

An alternative method is making a comparison between the movements of cash in an ordinary annuity and that of the annuity due.

• For an ordinary annuity = P + P (1 + r) ………P (1 + r) n – 1
• For an annuity due = P (1 + r) + P (1 + r) 2 ………. P (1 + r) n

When (1 + r) is factored in, the annuity due cash flow becomes equal to the ordinary cash flow.

To conclude

The formula that we have used here is easy to understand and can be used in various stages of life.

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