Debt Consolidation Loan

Do you have a car payment to make each month? Do you pay rent on an apartment? Both of these are annuities! As you may have guessed, an annuity is simply a series of equal cash flows equally spaced out in time. There are two main types of annuities--ordinary annuities and annuities due.

An ordinary annuity is one in which the cash flows occur at the end of the time period. For example, if you start a new job with a monthly salary of $3,000, you receive your check for this amount at the end of the month. The fact that the cash flow (your salary in this case) is received at the end of the period along with the fact that it is the same value each month makes this an ordinary annuity.

So what in the world is an annuity due? It is just a series of equal cash flows that occur at the beginning of the period. My guess is, you're probably sufferring through an annuity due as we speak. If you are living in an apartment, making those rent payments, you're paying an annuity due. When you pay your rent on the first of the month, you're paying for the month ahead of time. That is, on August 1st, you pay rent for the right to live in the apartment for the rest of the month of August. This is an annuity due because the payments occur at the beginning of the period.

Let's look at a simple example of an ordinary annuity. If you deposit $1,000 at the end of each year into an account earning 9% compounded annually, how much will you have in the end of 5 years? Lets look at this on a timeline:

On our timeline, we see the $1,000 payments going into our account. The numbers of the bottom refer to the end of the year. I think after drawing the timeline, we're ready to put this into our financial calculator. We have 5 years, 9% interest, no present value (see the timeline at time period 0?), and $1,000 payments.

If all went well, your calculator should have given you a future value at time period 5 of $5,984.71. You may be wondering why we put the $1,000 payments in as a negative number. The reason for this is that these are cash outflows. A good rule of thumb is that if money is leaving your wallet, we put it in our calculator as a negative number. When money is coming back to you, it is a positive number. This problem also taught us a great lesson in that when we deal with ordinary annuities, the calculator will give us our future values in the final year of the annuity. In other words, the future value we just calculated is at year 5 on our timeline.

Now let's look at an annuity due (begin mode) problem. How much would you be willing to pay for an annuity that paid you $1,000 at the beginning of the year for 3 years if your opportunity cost is 11%?

Normally, the word "begin" makes your heart race and your hands sweaty. It really isn't that bad though. Again, we draw a timeline.

The first thing that you should notice about the timeline above is that we start at year 1 instead of year 0. When we're dealing with an annuity due, the numbers on our timeline represent the beginning of the year. So the 1 tells you that the $1,000 payment occurs at the beginning of year 1. We're going to handle this annuity due the same way we would handle an ordinary annuity. The only difference is that we will set our calculator to begin mode.

Piece of cake! Your calculator shows you that you'd be willing to pay $2,712.52 today for this annuity due. You've gotten the hang of annuities now, so try these practice problems on your own.

Practice Problem 1
If you deposit $100 at the end of each month into an account earning 11.5% annually, how much will you have saved at the end of 25 years?

Solution
Wow! You've saved up $172,011.55. If you're not getting the same answer that I do, make sure your calculator isn't in begin mode.

Practice Problem 2
How much would you have to deposit at the beginning of each month to have $10,000 saved at the end of the year? Assume your account earns 4% compounded annually.

Solution
Only $815.45 a month!

We can't fit everything into these tutorials, folks. If you want to discuss it further, please visit the UnderstandFinance forums.

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