Using the annuity factor, you can determine the future value of an annuity using a pretty basic formula. When people consider purchasing annuities, they are often hit with hundreds of choices and are really looking for advice, not options. Of course, they would like to know what their investment today would yield in the future. To determine this, we use the annuity factor to tell the customer exactly what their investment will be worth in the future.
Annuity Factor Formula
To compute the basic formula, you will require three pieces of information. This can get more complicated if interest is compounded monthly or there are additional payments made into the annuity, but this basic formula can be manipulated to cover nearly any scenario:
Present Value (PV): The present value is basically the amount of money you are starting the annuity with. If you start the annuity with $100,000, the present value is $100,000 as you have not earned any interest yet.
Interest Rate (i): Most annuities compound monthly, but to simplify our equation, we will assume the interest compounds annually. Simply, if you start with $100,000 and receive a 5% interest rate, your investment will be worth $105,000 in one year.
Number of Years (n): This is the number of years you want to compute the investment for. The annuity factor formula can work with any number of years and can be changed to include monthly interest compounding and/or additional monthly or annual payments into the fund.
For the math inclined, here is the entire annuity factor formula:
Future Value = PV(1 + i)^n
That is the entire formula, please read below for an explanation and an example.
So we know that if you invest $100k at 5% interest your investment will be worth $105k after one year. However, what happens after year two? If you said the investment would be worth $110k, you would be wrong. After year one you would receive your 5% interest payment on your initial investment of $100k. However, after year two you would receive your 5% interest payment on your initial investment, plus 5% interest on the first year’s $5,000 interest payment. In other words, the year two return would be $105,000 * i = $5,250. Of course, the year three return would be the original investment, plus the year one interest, plus the year two interest, multiplied by the interest rate. Or, $100,000 + $5,000 + $5,250 = $110,250 * .05 = $5,512.50 + $110,250 would give us the total amount our investment is worth at the end of year three ($115,762.50).
To simply this math, we can use the annuity factor and make the equation Future Value = PV(1+i)^n look like:
Future Value = $100,000(1+.05)^3 or $100,000 * (1.05*1.05*1.05) = $115,762.50
Future Value of an Annuity | Compounding Interest Monthly
In the interest of simplicity, I will spell out every step in this equation. There are quicker ways to compute the same thing, but this way should work for everyone that has forgotten algebra.
Present Value: The present value does not change; it is still your initial investment of $100k.
Interest Rate: If you have an annual interest rate of 5%, you can simply divide that by 12 to get your monthly interest rate. So, .05/12=.004167 (rounded). Therefore, we know that your $100k investment will be worth $100,417 after one month.
Number of Periods: Instead of computing the number of years, we have to change this to the number of periods. In this case, it would be the number of months you want to compute for. In keeping with our original example, we will choose 36 periods or three years.
Our annuity factor equation has to change to reflect the monthly interest rates, but everything else will remain unchanged.
Thus our new equation will be:
Future Value = $100,000(1+.004167)^36 or $100,000 * 1.16 = $116,149
At this point you should be able to determine the annuity factor for nearly any scenario. You can easily change any of the numbers to make the decision that is best for you or make further computations to factor in monthly or annual contributions. This article is designed to give you just the basics about how to calculate the annuity factor, please feel free to leave a comment if you would like to learn more about additional equations for different scenarios.