**Formula of Annuity Due (Table of Contents)**

## What is Annuity Due Formula?

Annuity Due Formula can be defined as those payments which are required to be made at the start of each annuity period instead of the end of the period. The payments are generally fixed. There are two values for an annuity, one would be future value, and another would be present value. Either of below formula can be used to calculate Annuity due, depending upon what is sort for whether the present value or the future value.

**Present Value of Annuity Due Formula = P + P [ {1 – (1+r)**

^{-(n-1)}} / r]and

**Future Value of Annuity Due Formula = (1+r) x P [{(1+r)**

^{n}– 1}/r]Where,

- P is the Periodic Payment
- r is the interest rate for that period
- n will be a frequency in that period

### Explanation of the Annuity Due formula

Annuity refers to fixed frequent payment or receipt. There is two formula which is use and the first one is the present value which tries to compute the value of the annuity in today’s term and the second formula is future value where this will compute the future value of the annuity due.

Both formulae have similarities where the annuity amount per period is required, then frequency for which the annuity will be made is required and finally the rate of interest.

### Examples of Annuity Due Formula (with Excel Template)

Below are the examples for calculation of annuity due.

#### Annuity Due – Example #1

**Stephan has deposited $1,000 at the start of the year and is planning to invest the same every year until 5 years. The interest rate earn will be 5%. You are required to do the calculation of the future value of an annuity due.**

**Solution:**

Here we are being asked to do the calculation of the future value of an annuity due using the below information

For calculation of the future value of an annuity, we can use the above formula:

** **

Future Value of Annuity Due Formula = (1+5.00%) x 1000 [{(1+5.00%)^{5 }– 1}/5.00%]

**Future value of an annuity due will be –**

**Future value of an annuity=$ 5,801.91**

Therefore, the future value of the annual deposit of $1,000 will be $5,801.91

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#### Annuity Due – Example #2

**Mr. William wants to purchase a house after a couple of years. His target house value is $3,000,000. He decides to invest in a product where he can deposit yearly $600,000 starting at the beginning of each year until year 10. He wants to know what is the present value of the annuity investment that he is doing. This would enable him to know what the true cost of the property in today’s term is. You are required to do the calculation of the present value of the annuity due that Mr. William is planning to make. Assume that rate earned on investment will be 12%.**

**Solution:**

Here, Mr. William is making an annual investment of $60,000 in order to achieve the goal of purchasing the property which values around $3,000,000.

We are given the principal amount, the frequency of investing and rate of interest, and therefore we can use below formula to calculate the same.

** **

Present Value of Annuity Due Formula = 60,000 + 60,000 [{1-(1+0.12)^{-(10-1)}}/12%]

**Present Value of Annuity Due will be –**

Present Value of Annuity Due = **$ 3,796,949.88**

It appears that by investing $600,000 yearly in the product, Mr. William would be easily able to purchase the house which is he is planning for.

#### Annuity Due – Example #3

Company X is a highly capital-intensive invested company. It imports most of the machinery from foreign countries as it is cheaper compared to buying from the local market. The company plans to set aside an amount of $118,909 semi-annually starting now. As per the recent market trends, the average revenue earned on the investment is 8%. The company expects to fund the machinery after 15 years where they expect the value of the machinery to be $7,890,112. The company wants to know what the future value of the investment shall be, and will they be able to fund it or they would require funds in the form of a loan.

You are required to do the calculation of the future value of the annuity investment done by the company and compute the amount of loan if the company requires it?

**Solution:**

In this example, the company is trying to keep aside funds for replacing the machinery in the future and avoid any Adhoc fund requirement in the form of costly borrowing.

The frequency here is semi-annually, the payment every period given is $118,909 and period will be 15*2 which is 30 years. Rate of interest will be 8/2 which is 4%

We can use the above formula to calculate future value.

Future Value of Annuity Due Formula = (1+0.04) x 118,909 [{(1+0.04)^{30}-1}/0.04

**Future value of Annuity will be –**

**Future value of annuity =** **6,935,764.02**

The value of the machinery is $7,890,112 and the return from investment amount is $6,935,764.02 and therefore the company will be required to borrow loan which shall be a difference of these which is equal to $954,347.98.

### Relevance and Use

An annuity due formula will require payments to be made at the start of the period, contrary to the end of every period of an annuity. An individual who is legally entitled to annuity due payments represents it as an asset. On the flip side, the individual who is required to pay the annuity which is due shall have a legal debt liability that requires timely payments.

Because a series of annuity due payments represents a number of cash inflows or outflows which shall occur in future, the recipient or the payer of the funds would like to compute the wholesome value of the annuity while accounting for the time value of money. This can be accomplished by using the present value of an annuity due.

### Recommended Articles

This has been a guide to Annuity Due Formula. Here we discuss how to calculate future and present annuity due with its formula and examples. You can learn more from the following articles –

- Formula of Deferred Annuity
- Annuity Formula Calculation
- Annuity vs Perpetuity – Compare
- Annuity vs Lump Sum – Compare

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