Future Value of Annuity

The future value of an annuity is a calculation that measures how much a series of fixed payments would be worth at a specific date in the future when paired with a particular interest rate. The word “value” in this term is the cash potential that a series of future payments can achieve.

The payments in a typical annuity are distributed at the end of a pay period. An example of this would be a company that pays out dividends at the end of a fiscal quarter where its earnings allowed them to pay proceeds to shareholders. This is not to be confused with an annuity due, where payments are distributed at the beginning of a pay period.

When you are calculating the future value of an annuity, you are looking at the total sum of all the payments made during that time period as well as the interest they would accumulate. You could take the time to create a table that lists all the payments made, the individual pay periods, and the interest each payment would accumulate to find the sum total of both payments and interest.

Thankfully, the future value of annuity formula provides a much simpler solution to finding this cash value. This formula can help you make quick decisions when determining the worth of an investment. 

Future Value of an Annuity Formula

$$FVA = C \times \bigg[\dfrac{(1 + r)^{n} - 1}{r}\bigg]$$

  • C = cash value of payments made per period
  • n = number of payments
  • r = interest rate

For this formula, the cash value of all payments must be equal and the interest rate would need to stay consistent during the lifetime of the payments. If the payments are unequal from payment to payment, or if the interest rates will change over time, there isn’t a special way to calculate the future value. In this case, you would need to construct a table as mentioned above to calculate the future value. 

Future Value of an Annuity Example

You have an investment account that has a 6% annual interest rate. At the end of each year, you invest an additional $2000. You want to know how much you will have in your investment account over the next 5 years. 

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

  • Number of Payments (n): 5 
  • Cash value of payments made per period (C): 2000
  • Interest rate (r): 6% or 0.06
  • Future Value of Annuity (FVA): Unknown

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

$$FVA = 2000 \times \bigg[\dfrac{(1 + 0.06)^{5} - 1}{0.06}\bigg] = \$11{,}274.19$$

The formula can be broken down into the following steps:

  1. 1 + 0.06 = 1.06
  2. 1.06 to the 5th power = 1.338225576
  3. 1.338225576 – 1 = 0.338225576
  4. 0.338225576 / 0.06 = 5.63709296
  5. 5.63709296 x 2000 = 11274.18592

In this case, the future value of this annuity and the total cash value of your investment over the course of 5 years would be $11,274.19. 

Future Value of an Annuity Analysis

This FV calculation is an analytical tool to help estimate the total cost of cash installments. Companies can use it if they have an investment that will require more than one payment, and they want to predict the potential outcome of the investment.  

However, the most popular form of annuities are retirement annuities because of their promise to provide a steady stream of income over time, often through the life of the individual. They have multiple options which range from long-term investments to immediate payouts. However, the appeal of immediate or consistent payouts can blind individuals to the financial reality of their investment options.   

In any annuity, it’s important to calculate the cash value over time to make sure that it is the best financial option available to you. This is where the future value of an annuity calculation comes in as a valuable tool for average consumers. It allows people to be aware of how their investment is changing over time, so they can more accurately compare investment opportunities. 

Even the difference in the types of annuities can make a big difference in the outcome of an investment. An ordinary annuity versus an annuity due, for example, does not have as high of a present value (or current income generated by future investments). 

Also, this formula takes into account the time value of money. This means that money you invest now is worth more than money you invest later because the money you invest now is able to accrue interest for a longer period of time.

So if you invest $1000 today and $1000 next year, the money you invested today would have a greater value because it would have the opportunity to make money off of the interest it would accrue during the year. Because of this, ordinary annuities are directly affected by interest rates. If interest rates rise, the future value goes down. If interest rates fall, the future value increases. 

Future Value of an Annuity Conclusion

  • Future value of an annuity is a tool to help evaluate the cash value of an investment over time. 
  • Future value of an annuity is primarily used to measure how much that series of annuity payments would be worth at a specific date in the future when paired with a particular interest rate.
  • The calculation of future value uses 3 variables: the cash value of payments made per period, the interest rate, and the number of payments. 
  • The FV calculation is only effective with a fixed interest rate and equal payments during the set time period. 

Future Value of an Annuity Calculator

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

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