Future Value of an Annuity Due

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Future value of an annuity due is used to predict the future value of a series of payments where the payment is made immediately at the beginning of the payment period. The payment at the beginning of the period is the main difference between an annuity due and an ordinary annuity.

Let’s quickly recap what an annuity is. An annuity is a set of payments made in a series over a certain period of time. They can either be payments made to a financial institution or business, or they can be payments sent out to the individual.

There are two main types of annuities:

  • Ordinary annuity. There is an ordinary annuity, in which payments are made at the end of a pay period. An example of this would be companies paying dividends to shareholders.
  • Annuity due. The second type of annuity is known as an annuity due. This is the type of payment we are focusing today and an annuity due requires the payment to be made at the beginning of the payment period. The payment typically covers the balance owed for the remaining period following the payment. 

The future value of an annuity due formula is used to predict the end result of a series of payments made over time, including the income that is made from their associated interest rates. The term “value” refers to the potential cash flow that a series of payments can achieve. So by looking at the future value, we are calculating this potential at a future date in time. 

It is possible to calculate the future value of an annuity due by hand. To do this, you could make a chart to list the amounts of the payments being made. You would identify the payment periods and the set interest rate through the time limit you have set. However, this would take a lot of extra work and time. Thankfully, the formula can help you promptly find the answer. 

Future Value of an Annuity Due Formula

FV = C \times \bigg[ \dfrac{(1 + r)^{n} -1}{r} \bigg] \times (1 + r)
  • C = cash value of payments made at the beginning of each pay period
  • r = interest rate
  • n = number of payments

Future Value of an Annuity Due Example

Michelle sees an ad for a 3 bedroom house available, listed at $1800 per month. She wants to rent the property for three years, but the rent is $9600 per year more than she is paying for her rent now in her apartment. 

Before she signs a lease, Michelle wants to know how much money she would have in three years if she were to stay in her current home and invest the additional $9600 per year in an account with a 5% annual interest rate. 

Let’s break it down to identify the meaning and value of the different variables in this problem. 

  • Number of Payments (N): 3 
  • Cash value of payments per period (C): 9600
  • Interest rate (R): 5% or 0.05
  • Future Value of an Annuity Due (FV): Unknown

We can apply the values to our variables and calculate the future value of this annuity in 5 years.

FV = 9600 \times \bigg[ \dfrac{(1 + 5\%)^{3} - 1}{5\%} \bigg] \times (1 + 5\%) = \$31{,}777.20

The formula can be broken down into the following steps:

  1. 1 + 0.05 = 1.05
  2. 1.05 to the 3rd power = 1.157625
  3. 1.157625 – 1 = 0.157625
  4. 0.157625 / 0.05 = 3.1525
  5. 1.05 X 9600 = 10080
  6. 10080 x 3.1525 = 31777.2

In this case, the future value of this annuity and the total cash value of Michelle’s investment over the course of 3 years would be $31,777.20.

That would certainly be a sizeable investment if Michelle were able to stay in her current apartment for the next three years.

With this knowledge, Michelle can make a more accurate decision between the two locations. She can weigh out her choices: is it more important for her to have the $31,777.2 saved? Or is it more important for her to live in a bigger more luxurious space?

Whatever she decides, at least she has a better understanding of the future value of the monthly payments she would be making. 

In order for Michelle to achieve this return, she would also have to make her first year’s investment of $9600 at the beginning of the year. This means she would need to have $9600 saved upfront to either invest or parce out towards the new (higher) rent for the house.  

It is important to note that, in this formula, the interest rate must remain the same through the series, and payment amounts must be equally distributed. If the payments differ during the series, or if the interest rates will change over time, there isn’t a formula to calculate the future value of that particular annuity due.

Future Value of an Annuity Due Analysis

This future value of an annuity due formula is an investigative tool that is used to estimate the total value of cash payments made at the beginning of a pay period. 

It’s important to understand the difference in the types of annuities you are calculating because there can be a substantial change in the ultimate result of an investment depending on the type you use. An annuity due, for instance, will have a higher present value because you would be making these payments at the beginning of the pay period. 

Because of this, this formula accounts for the time value of money. Essentially, the money you invest immediately has a greater worth than money you invest later because it is able to gather interest for a greater amount of time. 

Additionally, in an annuity due, the payee often has a legal responsibility to make the payments, like Michelle in the example above, The formula can be used to in the decision-making process of whether or not to enter into a legally binding agreement. 

Future Value of an Annuity Due Conclusion

  • The future value of an annuity due is a tool to help evaluate the cash flow potential of a financial investment. 
  • Future value of an annuity due is primarily used to assess how much that series of annuity payments would be worth at a specific date in the future when paired with a particular interest rate.
  • All the payments made in an annuity due must be paid at the beginning of the period. 
  • The formula identifies 3 variables: the cash value of payments made per period, the interest rate, and the number of payments within the series. 
  • The FV of annuity due calculation is only effective with a fixed interest rate and equal payments during the set time period.

Future Value of an Annuity Due Calculator

You can use the future value of an annuity due calculator below to quickly work out the potential cash flow of monthly payments by entering the required numbers.