A personal finance blog dedicated discussing such topics as budgeting, asset allocation, 401K, IRA, cash flow, insurance, financial planning, portfolio management, and other areas in personal finance.


Friday, July 15, 2005

How to Calculate the Present Value of an Annuity

It is amazing how the math we all thought was useless back in high school is really pretty useful today. Understanding mathematical concepts is very important in understanding personal finance. It is also very liberating to be able to do different "complex" calculations with the aid of a spreadsheet.

Today I want to show you how to calculate the present value of an annuity stream. Huh? Well, before you zone out or click away from this post, let me start with a question: Say you want to live on $50,000 per year from your investments once you retire. Let's say you are going to retire at age 60 and expect to need the money for 25 years. We will also say that you expect to get a 5% return on your money. Now, how much money do you need at age 60 to be able to meet your goal?

Well, if you were to put all your money under your mattress where it got zero return, you would need $1,250,000 ($50,000 X 25 years = $1,250,000). You would stick $1,250,000 under your mattress and each year take out $50,000 to spend. At the end of 20 years, you would have nothing left.

However, if you are like most people, you probably want to get some sort of return on your money. This makes the calculation more difficult but not impossible. As we said earlier, let's say you expect to get 5% per year on your money. To do this calculation, we have to use the following formula:

(1/i) - [1/(i X (1 + i)n)]

The "i" stands for expected interest rate, which is 5% (.05). The "n" stands for the number of periods, which is 25 years. The "X" is the multiplication sign. So, using real numbers, the equation would look like this:

(1/.05) - [1/(.05 X (1 + .05)25)]

20 - [1/(.05 X 3.3863549]

20 - [1/.1693177]

20 - 5.9060554


14.0939446 is our "factor." To get the amount of money we need at age 60 to fund this income stream, you multiply $50,000 by the factor (14.0939446). So, for this example, we need $704,697 in the bank at age 60 in order to fund an annual income of $50,000 for 25 years. IMPORTANT NOTE: At the end of 25 years, the money will be gone!

Was this helpful? Let me know by leaving any questions or comments. In a future post, I'll show you how to do this same calculation with a spreadsheet.

UPDATE: Here's a link to a follow-up post to this one.

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