Future Value of an Annuity

Finding the future value of an annuity is not a calculation best left to financial advisors.  Any time an individual makes a payment on a loan, a lease, life insurance, credit cards, or even rent, mathematical formulas to find the future value of an annuity could be used to understand the total actual cost of these items; including interest.  For investment purposes, the future value of an annuity will determine how much to invest today. 

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Explanation of Annuities

An annuity is an investment or retirement vehicle that requires contributions in exchange for future income.  Fixed payments are made at a specific frequency for a set period of time, at a certain rate of interest.  Annuities are contracts between individuals and insurance companies that help to mitigate the risk of a consumer outliving their assets.  It is fundamentally different from life insurance in that an annuity provides income while you are alive, and life insurance provides benefits only upon your death. 

Annuities have distinct benefits, including the feature of tax deferred growth.  All principal payments made to an annuity are not taxed; taxes are only assessed on the actual earnings of the annuity, and are only applied when the annuity is being paid back to the investor.  Additionally, some annuities offer death benefits that may be paid to designees in the event of the principal account holder’s passing.

Types of Annuities

There are two types of annuities: an Ordinary Annuity, which requires payments at the end of each period, and an Annuity Due, which requires payments at the beginning of each period.  When finding the future value of an annuity, each type will require its own set of formulae and calculations.  Furthermore, either of these annuities can be one of three subtypes.   

A Fixed Annuity is one where the contribution amount and the payout amount are fixed and guaranteed.  Conversely, a Variable Annuity is a vehicle where the payout depends upon the performance of the annuity’s investments.  This means that a strong market will realize higher annuity income, while a weak market will result in smaller payouts.  A third type, called Equity Indexed Annuities, provide a return that is index or market based, but still guarantees a minimum level of return.

All annuities are either deferred or immediate in payout.  Deferred annuities have smaller contribution payments over long periods of time, while immediate annuities require a large initial payment in exchange for immediate income. 

Understanding and Calculating Future Value

Future value of an annuity refers to the amount of money accumulated after all set payments have been made for a specific period of time with interest compounded.  For instance, if a loan is acquired that calls for a monthly payment of $500 at a 6% rate of interest for 5 years, then the future value would be the total of all money paid at the end of the 5 year period.  From an investment standpoint, the future value of an annuity would be the total value of the annuity after all payments have been received and interest has been added. 

As an example, consider the following ordinary annuity: payments are $8,000 per year at 6% interest for 5 years.  In order to determine to future value of this annuity, the total payments would need to be added to the total compounded interest over the term of the annuity.  This is best expressed by the following formula:


FVOA =   P      (1 + i)^n – 1
                                i

This formula assumes that “FVOA” = future value of ordinary annuity, that “P” = payment amount, “I” = interest, and “n” = the amount of time.  Therefore, we must break down the formula as shown above into manageable segments.  In the case above, the figures are as follows:
P = $8000
i = .06
n = 5

We can then write the equation out like this, keeping in mind that the interest must be written in decimal format: 


FVOA = $8000   (1.06)^5 – 1
                                 .06

The next step is to solve for the above, where the carat indicates a raised power:

1.06^5 = 1.338225576 – 1 = 0.338225576 / .06 = 5.637 * $8,000 = $45,096

So in this case, the total principal invested in the annuity was $40,000, and the annuity realized returns of $5,096.  The future value of this particular annuity is $45,096.  Using this formula, it becomes apparent that an annuity is a valuable investment tool.  However, it should be noted that there are fees and other costs associated with annuities, so it is important to calculate whatever those fees are and subtract them from the principal contribution amount of the annuity after the future value has been determined. 

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Finding the future value of an annuity due is slightly different.  Because an annuity due collects payments at the beginning of each period, the account begins to earn interest faster than an ordinary annuity.  For example, in an ordinary annuity, the first payment is made at the end of the first period.  This means that there was no interest collecting during the initial term of the first period.  With an annuity due, the account is opened with a payment at the beginning of the period, resulting in interest being compounded for longer during that period and overall for the duration of the annuity.  To account for this difference, the formula is as listed below.  Keep in mind that all symbols retain their meaning, except that FVOA becomes FVAD, for future value of annuity due.

 
FVAD =   P     (1 + i)^n – 1   X  ( 1 + i )  
                               i              

For this example we will use the same figures to show the difference in future value between an ordinary annuity and an annuity due.  The above formula would be broken down like this:


FVOA = $8000     (1.06)^5 – 1  X  ( 1.06 )
                                    .06

The equation would be solved for the future value of the annuity accordingly:

1.06^5 = 1.338225576 – 1 = 0.338225576 / .06 = 5.637 * $8,000 = $45,096 X 1.06 = $47,801.

This clearly demonstrates that the compounded interest will have a substantial impact over the life of the annuity due, just as compounded interest on credit cards means significantly more expenses for consumers.  In effect, an annuity can be viewed as a reverse loan- one where you pay money to an organization now with the agreement that they will pay you back, with interest. 

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